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In the second round on Tuesday, Kirber booked his ticket to beat Italy's Camilla Georgi 7-6 (7-3), 6-2, and Bertens pulled out Spanish rival Garbini Mogorutsa.
In the first set, Kirper faced a difficult set and needed a break to put himself in his favor before easily winning a second 6-2, ending the match in his favor in an hour and 47 minutes. minutes.
It's Kirber's fifth win over Georgi in five games.
"It's always hard to play against Camilla and the way you hit the ball," she said, "It's never easy to play the first game, but I'm happy to qualify." "
In the next round, Kirber will meet Czech Petra Kvetova, fifth with the invitation card or Su-Wai Hsieh, as she faces Sloane Stevens (fourth) or Yulia Potentsiva (Kazakhstan).
Kvetova began her career in the tournament, which won her title in 2015, beating Belarusian Arina Sabalinka 6-1, 7-5 on Tuesday.
Covitova, a two-time Wimbledon champion, needed 79 minutes to clinch her third win in five games against Sabalinka, who won the Chinese title at the expense of American Allison Risk.
Kvitova rebuked Sabalinka at the 32nd US Open at Flushing Meadows last summer.
Hessier defeated American Daniel Collins 7-6 (7-4), 6-3.
Stevens avoided the early exit after missing a blank set and was one point behind the loss of the second and match against Russian Ekaterina Alexandrovna, but saved the situation and ruled in his favor 7-6 (7-3), before winning the third after a break also 7-6 (7-3)
"I was like I would not lose even worse," said Stevens about the first set. "Obviously, she played well, and sometimes when you play with a player who plays that way, you can not do much."
Daria Katastina, Russia, Alexandra Sasenovic, Belarus, 1-6, 4-6
In the second round of the match, Sasenovic will meet Australian Prizella Hoon, who beat German Tatiana Maria 6-3, 7-6 (7-4).
Ashley Barty, second-place champion, defeated Latvia's Yelina Ostapenko 6-3, 6-3.
In men's singles, Australian Jordan Thomson beat Jordan's Taro Daniel 3-6, 7-6 (7-5), 6-0.
Frenchman Luca Boyi, 6, and Jeremy Chardy, 6-1, 6-2, 6-1, and Andrei Robleve, Russia, 2-6, 3-6.
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