Rafael Nadal has turned his focus to the ATP Finals after his shock exit from the Paris Masters, though found it hard to visualise success in Turin.

World number two Nadal crashed out in the second round of the ATP 1000 event on Wednesday, going down 3-6 7-6 (7-4) 6-1 to Tommy Paul.

Nadal, who was contesting his first match since his Laver Cup doubles exhibition with the now-retired Roger Federer, took the opening set and appeared on his way to a comfortable victory when he went up a break in the second.

But Paul broke straight back, going on to win the tie-break before storming home in the decider as Nadal seemed to struggle physically the longer the match dragged on.

Speaking to the media after the loss, Nadal gave credit to his opponent and said he did not deserve to win after blowing his chance.

"It's okay – all the credit to Tommy," he said. "Things happen sometimes.

"I think he played aggressively, a lot of great shots. I had my match in that second set, with a set and break [lead]. 

"I played a terrible game there. I didn't deserve the victory playing that bad in that key moment, no.

"Until that moment, it was okay, a good match for me. Knowing that this is my first match in a while – and this surface especially, you cannot make mistakes with your serve.

"We are always ready to find excuses, but in the end, it's always the same. You play well, you win; you don't, you lose. 

"For moments, putting everything in a pack, I was playing quite well. Then at the right moment, I didn't make the right things. So that's it – he played well, he's having a great year."

Turning his attention to the season finale in Italy, Nadal said he will be there if everything goes to plan.

"Yes, I hope, if nothing happens, I hope to be there," he said. "I'm excited about playing, even if it hasn't been the perfect couple of months for me, of course. 

"But yeah, nothing to lose. After a good year, going there, just trying my best. It's true that for the last five months I didn't spend enough days on the Tour.

"I don't even say competing on a tennis court – I say on the Tour. Practicing with the guys, that's what I need."

His lack of a strong build-up to the tournament has 22-time grand slam champion Nadal admittedly not liking his chances, saying it would be "difficult to imagine" this being the year he is able to win his first ATP Finals title.

"I mean, for me it's difficult to imagine now arriving in good enough shape to win a tournament like this one that I didn't win during my whole tennis career," he said.

"To play against the best players of the world, from the first day you need to be there and the rhythm, conditions, that will not happen. 

"So the only thing I can do is try to be there earlier, have some good practice with the guys and then give my best on the court – and hopefully the level of tennis will be there, and the body too.

"I can't predict much, and I honestly don't think much about what I have to do or what I don't have to do to be really there. 

"I just think about 'be better' – I need to improve a couple of things, and then I need to play sets against the best players, to feel myself again, competitive against everyone.

"That's it – I'm gonna try to make that happen – and if not, you know what, there's going to be next year, and I'm going to try to have the best season possible to start strong."

Carlos Alcaraz views fellow Spaniard Rafael Nadal as another competitor and "not my enemy", despite the pair's battle for top spot in the world rankings.

The 19-year-old continues to break records at the top table in tennis, becoming the first teenager to be crowned world number one in the Open Era.

Alcaraz, aged just 19 years and 129 days, also set a new benchmark as the youngest number-one ranked male player in the world since rankings were published in 1973.

Those feats came after winning September's US Open, where he joined Arthur Ashe (1968) and Rod Laver (1969) as the only Open Era players to win on their first or second main-draw outing at the tournament.

Now, Alcaraz has Nadal – a record 22-time major winner – chasing him for top spot, though the youngster assures there will never be bad blood between himself and his compatriot.

"I don't see it that way," Alcaraz responded to Eurosport when asked if he was embroiled in a battle with Nadal.

"It's true, Rafa is fighting for the No.1. Some players have the same goal – to be No.1, so I need to do my best. Outside the court [Rafa and I] are colleagues, at least it's the way I see it.

"Rafa is not my enemy. I say hello, I don't see that competition. With the rest of the players, it's the same. Beyond that relationship, I'll try to keep being No.1."

While Alcaraz remains the world's top-ranked male player, he intends to savour the moment after a surreal victory at the US Open.

"It is an incredible feeling, waking up as No.1, the US Open winner. It's a dream come true," he added.

"I am enjoying this moment so far. I keep working, my life is still the same, I'm still the same kid, same player. I just keep practising, keep improving."

As the teen aims to relish topping the ranks, his next focus turns to the Paris Masters – where he faces Yoshihito Nishioka on Wednesday – with a knee injury not as serious as first thought.

"It's a little pain, but the calendar is very demanding," he said of the injury. "We are playing and travelling with barely any breaks and it's normal that we have a few pains.

"All players have them and we learn how to deal with them. I am feeling good physically and I am ready to play here in Paris and in Turin in the [ATP] Finals."

Daniil Medvedev celebrated "one of the best victories" as he beat Denis Shapovalov 4-6 6-3 6-2 in the final of the Vienna Open on Sunday.

Playing in his first tour-level final since winning the Mexico Open in August, Medvedev found himself on the back foot after Shapovalov came out on top in a 50-minute opener.

The world number four conceded serve twice in the first set – the first time he had been broken throughout his run in Austria.

However, Medvedev hit back to claim the second set at the first time of asking.

Having lost serve twice in the decider, Shapovalov hung on in to frustrate Medvedev, saving six match points before finally succumbing to a deft drop-shot that the Canadian could only clip back into the net.

The victory marks Medvedev's second title of 2022, while it also ensures the Russian – who worked his way to world number one earlier in the year – will play in the ATP Finals next month, after going for glory at the Paris Masters.

"This match was the best of the week because Denis was really playing unreal until probably 4-3 in the second set," said Medvedev, who is aiming for a strong end to the season.

"He dropped his level by maybe two per cent and I was able to use it. This is one of the best victories when you know your opponent is on top of you, but you try and stay there and do what you can.

"I like to play indoor hard courts at the end of the season. I feel that I do a great job with my team not to arrive burnt out.

"I'm looking forward to the last two tournaments of the year which are really important and I usually play well."

World number one Carlos Alcaraz was stunned in the Swiss Indoors Basel semi-finals as Felix Auger-Aliassime set up a final clash with Holger Rune.

Auger-Aliassime saw off the US Open champion in just 82 minutes as he won 6-4 6-3 to take his unbeaten run to 12 matches.

The Canadian was in irresistible form on Saturday, with his shot placement in decisive moments proving far more consistent and lethal than his counterpart, hitting 23 winners to Alcaraz's eight.

Twenty-two-year-old Auger-Aliassime is still fighting to qualify for the ATP Finals for the first time and victory in Sunday's final will move him up to sixth in the rankings having won each of his two previous tournaments in Antwerp and Florence.

"It's amazing," Auger-Aliassime said. "I never expected it, when I was in Florence three weeks ago, or after the US Open. I'm just really happy that all my work is coming together.

"I've always believed that I can play this way, that I can be consistent in that way, but one thing is to believe and the other is to actually do it. It's nice to feel that way, it's nice to come out on the court and win that many matches in a row. So hopefully this is just the beginning of seeing me play this way."

Rune awaits after the Dane beat Roberto Bautista Agut 7-6 (7-1) 7-6 (10-8) despite being 6-2 down in the second-set tie-break. He will move into the top 20 for the first time as a result of that win.

The final of the Vienna Open will be contested by Daniil Medvedev and Denis Shapovalov, who came through their respective semis in straight sets.

Top seed Medvedev was exceptional against Grigor Dimitrov, with the Russian's serve proving especially important in his 6-4 6-2 win.

Medvedev won 87 per cent of points on his first serve to leave Dimitrov frequently struggling for momentum, and the former world number one recognised that impact.

"The serve is probably the most important shot in tennis," he said. "I was lacking it a little bit this season, I was doing too many double faults. Sometimes in important moments my serve could have been a little bit better. I was working a lot with my coach to try and find this rhythm [again], and so far I'm serving good here. I'm really happy about it and that's also why I'm playing so good."

Shapovalov ultimately romped to an impressive win over Borna Coric.

A tight first set was followed by the Croatian getting bageled as Shapovalov won 7-6 (7-4) 6-0 to reach his second final of the year.

Novak Djokovic expects to find out in the "next few weeks" whether he can participate in next year's Australian Open and says the early signs are positive.

The 21-time grand slam winner was denied the chance to defend his title in Melbourne in January after having his visa revoked because he was not vaccinated against COVID-19.

Due to Australian immigration laws, Djokovic – who was also blocked from taking part in this year's US Open – faced a potential three-year ban from entering the country.

However, with fewer than three months to go until the 2023 edition begins Down Under, Djokovic is still hopeful his ban is waived so he can obtain a visa.

Asked for an update on the situation, the Serbian told Sportal: "When it comes to Australia, there are some positive signs, but unofficially.

"We are communicating through my lawyers in Australia. In fact, they are communicating with the authorities in charge of my case. 

"I hope to have an answer in the next few weeks, whatever that answer might be. I am hoping for a positive one so I have enough time to prepare for the start of the season."

Djokovic has won nine titles at Melbourne Park, which is the most of any male singles player and the most he has won at any of the four majors.

Rafael Nadal won the event this year in Djokovic's absence, and the latter is desperate to get a chance to draw back level on grand slam titles won by competing in Australia.

"I really want to go there. I am over what happened this year and I just want to play tennis, it is what I do best," he said.

"Australia has always been the place where I have played my best tennis, the results speak for themselves, so I am always extra motivated to go there. This time even more so.

"I am waiting for the permission again. It's a good thing they have now opened the borders for the unvaccinated foreigners travelling to Australia. 

"I have that ban, I hope it will be lifted. As I said, it is not in my hands, I hope the people in the Australian government will give a positive answer, that is all."

Carlos Alcaraz reached the last-16 stage of the Swiss Indoors Basel by beating Jack Draper in three sets on Monday.

The number one seed lost the opening set but responded to take the following two and win 3-6 6-2 7-5.

Alcaraz dominated at the net, winning 30 of 39 points to edge out his opponent after more than two hours.

Elsewhere, at the Vienna Open, fourth seed Taylor Fritz overcame Yoshihito Nishioka in another three-set thriller.

Nishioka took the opener, and Fritz was staring down the barrel in a second-set tie-break before trailing by a break in the decider.

However, the American won the final five games to advance 6-7 (4-7) 7-6 (9-7) 6-3.

The comeback boosted Fritz's chances of making the ATP Finals, trailing Felix Auger-Aliassime by 315 points in the Race to Turin.

Third seed Andrey Rublev found life far easier as he beat Diego Schwartzman 6-4 6-1.

Felix Auger-Aliassime clinched the European Open title by beating Sebastian Korda in straight sets in Antwerp, replicating last week's Firenze Open triumph to maintain his strong run of form.

Auger-Aliassime swept aside J. J. Wolf to emerge victorious in Italy a week ago, and was in control from the start on Sunday as he beat another American to win his third ATP title of the year.

The Canadian seized the initiative when he broke Korda's serve to go 4-2 up in the opener, before saving two break points early in the second set.

Korda failed to conjure up another opportunity to break as Auger-Aliassime wrapped up a routine 6-3 6-4 win by holding to love.

Auger-Aliassime has responded brilliantly to his first-round exit at the Astana Open earlier this month, winning eight consecutive matches – six of them in straight sets.

Meanwhile, the 22-year-old has now won three of his past four ATP Tour finals, failing to drop a set in any of those victories after losing each of his first eight final appearances.

Auger-Aliassime's victory also represented a major boost to his hopes of reaching next month's ATP Finals in Turin, strengthening his grip on the final qualification spot for the tournament.

Dominic Thiem saved three match points before beating Hubert Hurkacz for the first time to reach the semi-finals of the European Open on Friday.

Thiem was on the brink of being knocked out by the top seed in Antwerp, but fought back to win 3-6 7-6 (11-9) 7-6 (7-4).

The 2020 US Open champion fended off all three match points in a second-set tie-break to take a thrilling quarter-final the distance and then came out on top in another breaker to advance.

Thiem will do battle with Sebastian Korda for a place in the final after the American emphatically defeated eighth seed Yoshihito Nishioka 6-0 6-2.

Richard Gasquet moved into the last four at the expense of David Goffin and will face Felix Auger-Aliassime, who came from a set down to beat Dan Evans.

Matteo Berrettini remains in the hunt to win the Tennis Napoli Cup on home soil after a 6-2 6-3 quarter-final triumph over Taro Daniel.

Top seed Pablo Carreno Busta crashed out in Italy, losing 7-5 6-2 to Miomir Kecmanovic, who will face Lorenzo Musetti after he got the better of Daniel Elahi Galan. Mackenzie McDonald will come up against Berrettini after getting past Zhang Zhizhen.

Stefanos Tsitsipas sealed a Stockholm Open semi-final spot with a 7-5 6-3 win over Mikael Ymer and will take on Emil Ruusuvuori, who eliminated Frances Tiafoe.

Holger Rune and Alex de Minaur meet in the other last-four match in the Swedish capital following wins over Cameron Norrie and Denis Shapovalov respectively.

Dominic Thiem saw off Francisco Cerundolo for the second time in the space of a week as he dug deep in the deciding set to win 6-1 1-6 7-5 at the European Open.

The Austrian downed the Argentinian in straight sets six days earlier in Gijon but found this a sterner test of his capabilities against the sixth seed.

Nevertheless, the former US Open winner shook off a second-set collapse and then responded to going a break down in the decider, winning four of the final five games to seal a quarter-final clash with favourite Hubert Hurkacz.

He was joined in the last-eight by two more unseeded players, as David Goffin and Sebastian Korda recorded straight-set upsets over third seed Diego Schwartzman and fourth-ranked Karen Khachanov respectively.

At the Stockholm Open, fifth seed Alex de Minaur made swift work of American J.J. Wolf, dispatching him in a 6-4 6-2 win to set up a quarter-final with Canada's Denis Shapovalov.

Defending champion Tommy Paul is out however, losing to Sweden's Mikael Ymer, who recorded a 6-2 6-3 victory that earns him a clash with top seed Stefanos Tsitsipas.

Slippery court conditions contributed to a backlog in fixtures at the Napoli Cup, meaning first-round matches were followed by second-round encounters on Thursday.

Nevertheless, second seed Matteo Berrettini made light work of Roberto Carballes Baena, winning 6-4 6-2.

Roberto Bautista Agut, seeded third, slipped to a 6-4 6-4 loss to Mackenzie McDonald, with the American joining Berrettini in the last eight.

Grigor Dimitrov crashed out of the Stockholm Open to the unseeded Jiri Lehecka in a three-set thriller on Tuesday, as Botic van de Zandschulp also fell at the first hurdle at the European Open.

Dimitrov, seeded sixth in the Swedish capital, came up short against Lehecka, who seized a surprise 6-4 1-6 7-6 (7-5) win, his first on the ATP Tour since July.

Victory for Alex de Minaur was far more predictable, a 150th at tour level coming courtesy of a straight-sets defeat of Benjamin Bonzi.

In Antwerp, Dominic Stricker handed Van de Zandschulp a swift exit, winning 6-2 6-4 to stay on Lehecka's coat tails in pursuit of a place at the Next Gen ATP Finals.

Stricker's reward for this win will be a second-round encounter with French veteran Richard Gasquet, who knocked out three-time grand slam champion Stan Wawrinka on Monday.

At the Napoli Cup, fifth seed Miomir Kecmanovic saw off wildcard Flavio Cobolli with ease, but others found life rather tougher.

Respective seventh and eighth seeds Albert Ramos-Vinolas and Adrian Mannarino fell to Nuno Borges and Pedro Cachin.

Holger Rune maintained his impressive form by beating Thiago Monteiro in straight sets to reach the second round of the Stockholm Open on Monday.

Rune was beaten by Marc-Andrea Huesler in the final of the last tournament he entered in Sofia following a quarter-final appearance in Metz.

The Danish teenager, who last week announced Patrick Mouratoglou had joined his team for the rest of this season, defeated Monteiro 7-5 6-2 on his debut in the Swedish capital.

Rune did not face a break point and won 86 per cent of points on his first serve as he booked a meeting with Cristian Garin.

Garin beat qualifier Jason Kubler 6-2 6-4, while Maxime Cressy and Aslan Karatsev advanced to the last 16 at the expense of Ilya Ivashka and Lukas Rosol respectively.

Richard Gasquet consigned Stan Wawrinka to an early exit at the European Open, coming from a set down to win 2-6 7-6 (7-4) 6-4 in a battle of two of the most experienced players on the circuit.

Fifth seed Dan Evans beat Tallon Griekspoor 6-3 6-4 in the first round in Antwerp, while his fellow Brit Jack Draper was an emphatic 6-1 6-2 winner against Jenson Brooksby of the United States.

J.J. Wolf was no match for Felix Auger-Aliassime in the final of the Firenze Open, as the Canadian won 6-4 6-4 in Florence.

Auger-Aliassime is targeting a place in the end-of-season ATP Finals and took a huge step towards securing such a spot on Sunday.

The top-seeded 22-year-old only dropped one set throughout the tournament and has now won his second ATP Tour-level title.

His victory over Wolf, the world number 75 who will rise to 56 on Monday, took only one hour and 41 minutes.

"It never gets old. Winning, it always feels like the first time," Auger-Aliassime, the new world number 10, said in his on-court interview.

"It's so special to win, especially here. I had a fantastic week and it's been amazing.

"Every final is tough, it's the two best players of the week. Of course you try to win more than you lose the finals, and that's why I came out here today ready to give everything.

"We had some very tough rallies in the second set, feeling tough physically. But you keep pushing, try to keep the level high.

"But there's no magic. Sometimes you win, sometimes you lose, but of course I'm really happy because I came here [as] the first seed.

"I was the favourite in all of my matches on paper. It's never an easy position, so to come out and win my four matches with confidence and conviction, it's really good for my confidence."

Wolf saved nine of the 12 break points he offered yet could not make any inroads against Auger-Aliassime's serve, with the champion winning without conceding on his service game.

Andrey Rublev defeated Sebastian Korda in straight sets in Sunday's Gijon Open final to land his 12th ATP Tour title.

The Russian had already prevailed in Belgrade, Dubai and Marseille this year and added another crown to his collection with a 6-2 6-3 victory against Korda in 75 minutes.

Top seed Rublev had dropped only one set in his three matches en route to the final and impressed against Korda with 29 winners, three breaks and just four unforced errors.

Korda, seeking a second Tour-level trophy following success in Parma last year, had his serve broken in the fourth and eighth games of the opening set.

Some heavy-hitting exchanges kept spectators gripped, though Rublev proved too strong for Korda in the second set and earned the only break in the sixth game.

Rublev got over the line with his fourth match point and remains sixth in the chase for an ATP Finals spot, with four of those ahead of him already qualified, along with Novak Djokovic. 

Andrey Rublev set up a final meeting with Sebastian Korda at the Gijon Open, overcoming Dominic Thiem in straight sets in the last four.

The world number nine battled through an up-and-down opener before remaining patient to seal the second set and the match on Thiem's serve, taking a 6-4 6-4 victory.

Russian Rublev has now won eight successive sets of tennis against the 2020 US Open champion, and he is one win away from his fourth title of 2022 after triumphs in Belgrade, Dubai and Marseille.

Speaking on court after the win, Rublev said: "I was lucky I played a really good game and Dominic helped me out a little bit.

"Then I felt more confident and I was able to win in two sets, which was the most important thing. This week I have been playing really well, and I'll try to show my best tennis of the week tomorrow."

Korda will be Rublev's opponent on Sunday after the American saw off France's Arthur Rinderknech for a 7-6 (7-2) 6-3 win.

Meanwhile, at the Firenze Open, top seed Felix Auger-Aliassime saw off home favourite Lorenzo Musetti 6-2 6-3, moving one step closer to a second ATP Tour title.

The Canadian will face JJ Wolf in the final in Florence, after the American clinched a 6-4 6-4 win over Sweden's Mikael Ymer.

Elina Svitolina gave birth to her and husband Gael Monfils' first child on Saturday.

The couple, who married in July 2021, have announced the arrival of daughter Skai Monfils.

Former world number three Svitolina and two-time grand slam semi-finalist Monfils announced last May they were expecting a baby girl.

Svitolina posted on Instagram on Saturday: "Ladies and gentlemen, please give a warm welcome to Skai Monfils.

"Can't thank enough my husband to live [through] this unforgettable moment with me."

Monfils wrote on social media: "I had the most amazing night of my life, which ended with the most beautiful gift around 6.00am.

"Elina was strong and brave. I can't [thank] enough my wife and God for this special moment. Welcome to the world my little princess Skai."