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She is the top-ranked American player left in the woman's draw but that matters not to Sloane Stephens.
The shock defeat of title-holder and top seed Serena Williams on Wednesday left the 21-year-old from Florida as her country's flag-bearer and she delivered on Thursday with a confident 6-1, 6-3 win over Slovenia's Polona Hercog.
With Venus Williams also a casualty on Wednesday and Alison Riske and Coco Vandeweghe both losing their second round ties on Thursday, only Stephens and, in the other half of the draw, 18-year-old wildcard Taylor Townsend, are left among the US contingent at Roland Garros.
Asked what it meant to her being the top-ranked American left in the draw, Stephens was adamant. "Means nothing," she said.
"I think it's the two top seeds (Serena Williams and Li Na) being gone, I mean, it means nothing. Every match is a tough match.
"Every match is going to be a battle. You have to go out there and compete. You have to go out and compete no matter what."
Seeded 15th, Stephens was solid on serve against Hercog apart from a brief blip in the second set when the Slovenian broke to get to 4-3, and she has yet to drop a set having defeated tough Chinese player Peng Shuai in the first round.
She next plays Ekaterina Makarova of Russia, who defeated Vandeweghe, for a place in the last 16.
Stephens enjoyed a breakthrough year in 2013 highlighted by a semi-final appearance at the Australian Open, a run into the quarter-finals at Wimbledon and fourth round spots at both the French and US Opens.
That left her ranked 12th in the world at the end of the year and set to break into the top 10 this year under the guidance of Paul Annacone, former coach of Roger Federer.
She won through to the fourth round in the Australian Open, but had bad first round losses at both Dubai and Doha before reaching the quarter-finals at Indian Wells and the third round in Miami.
With the women's tournament blown wide open after the defeats of Williams and Li, Stephens has the chance to make good on breaking into the top 10 and possibly reaching her first Grand Slam final.
But she is aware that she needs to remain fully focussed on her own game and never take any match for granted.
"Anyone can have a bad day. Like with girls extra things can happen. That's just how it is. That's just the game of tennis," she said.
"And obviously last year there was ?? what was it called? 'Wimblegeddon', like we had that, and that was crazy and also in Australia this year.
"It is what it is, and you have to go out and compete. And whether a top seed loses or top seed wins a tournament, you just focus on yourself and do the best you can."