How Nadal can be prevented from becoming world No 1 by Alcaraz and Ruud – updated heading into semi-finals

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The race for the world No 1 ranking in men’s tennis is going down to the wire with Carlos Alcaraz and Casper Ruud keeping their hopes live

Kyrgios explains his moment of craziness: “I honestly thought it was legal. I’m going to look like an idiot”

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The Australian described himself as “bone-headed” for a bizarre moment in his otherwise brilliant performance against Daniil Medvedev at the US Open

Medvedev on losing world No 1 spot: “It’s not nice, but it’s motivation to do better.”

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The Russian will be overtaken at the top after the US Open, with Rafael Nadal in pole position to return to No 1

Azarenka: Abuse of women players “happens right and left on the Tour”

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The former world No 1 praised the courage of players like Fiona Ferro, who has accused her former coach of rape and sexual assault

“I always carry this chip on my shoulder” Kyrgios wants to prove his big stage chops again against Medvedev

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The Aussie is beyond excited for another chance to prove the haters wrong in New York.

Azarenka to Ukrainian players: “I’ve had a clear message from the beginning: I’m here to try to help, which I have done a lot”

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The former world No 1 said she’s been working behind the scenes to try to help any player who’s been affected by Russia’s war in Ukraine

Yuan advances to make it four Chinese women in third round for first time

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Yue Yuan’s 6-3, 7-6 (6) win over Irina-Camelia Begu means she plays American Jessica Pegula, the No 8 seed in round three

A glimpse of the future in New York as Linda Fruhvirtova puts new sister act on the map

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Remember the name, the tournament and the year. The 2022 US Open marks the beginning of the Fruhvirtova sisters’ foray into Grand Slam tennis

‘I can’t expect to play in the final every Grand Slam – but I want to’ – Nick Kyrgios on his revised expectations

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The Australian has some big targets – but is trying to be as realistic as possible

Gauff sets up all-American third round against Keys

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Coco Gauff won against Elena-Gabriela Ruse 6-2, 7-6 (4) on Wednesday. She’ll face American Madison Keys, the No 20 seed, in the next round

Straight sets for Murray over Cerundolo after double-bounce chaos

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Andy Murray defeated Francisco Cerundolo 7-5, 6-3, 6-3 on Monday and will face the winner of the match between Australian John Millman and American wildcard Emilio Nava in the next round

Djere saves two match points to beat Gasquet and reach Winston-Salem semis

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Laslo Djere edged out Richard Gasquet 6-4, 3-6, 7-6 (6) on Thursday night. He’ll face the winner of the match between No 13 seed Jack Draper and Swiss qualifier Marc-Andrea Huesler in the next round

Marta Kostyuk books spot in semi-finals at Granby

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Marta Kostyuk won against Rebecca Marino 6-2, 4-6, 6-2 on Thursday night and will play Australian Daria Saville, the No 9 seed, in the next round

Cressy serves-and-volleys his way to Winston-Salem quarter-finals

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Maxime Cressy edged out Lorenzo Sonego 6-7 (4), 6-2, 7-6 (3) on Wednesday night. He’ll face Frenchman Adrian Mannarino in the next round

Maxime Cressy aces through to last 16 at Winston-Salem

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Maxime Cressy won against James Duckworth 6-3, 6-3 on Tuesday evening. He’ll face the winner of the match between Italian Lorenzo Sonego, the No 14 seed, and Chilean Alejandro Tabilo in the next round

Kvitova edges out Keys to make Cincinnati final for first time

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The Czech is now just one win away from a 30th career WTA title

Kvitova crushes Tomljanovic in Cincinnati quarter-finals

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Petra Kvitova defeated Ajla Tomljanovic 6-2, 6-3 on Friday afternoon in Cincinnati and will face American Madison Keys in the semi-finals on Saturday.

Tomljanovic advances to last eight at Cincinnati WTA 1000

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Ajla Tomljanovic overcomes Veronika Kudermetova in a three-set thriller on Thursday in Cincinnati. Petra Kvitova is next up for Tomljanovic in the quarter-finals.

Halep withdraws from Cincinnati, giving Kudermetova a free pass

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Veronika Kudermetova benefited from the withdrawal of Simona Halep on Wednesday in Cincinnati. Kudermetova got a free pass to meet Paula Badosa or Ajla Tomljanovic in the round of 16.

Fritz brushes aside struggling Kyrgios, into Cincy last 16

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Taylor Fritz beat Nick Kyrgios 6-3, 6-2 on Wednesday evening. He’ll face Russian Andrey Rublev, the No 6 seed, in the next round

Sinner gets retirement from Kecmanovic in Cincinnati second round

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Jannik Sinner benefited from the abandonment of Miomir Kecmanovic (7-5, 3-1) on Wednesday evening. He’ll face Canadian Felix Auger-Aliassime, the No 7 seed, in the next round