Bedanova had clearly watched and learned, so much so that she out-thought and eventually out-played the two-time US Open champion.

‘‘I hit with her before I even played my first tournament in Philadelphia,’’ said Bedanova. ‘‘It was a really great experience. Monica is a great person, really nice, and we practised a couple more times.

‘‘I wanted to have her as a mentor. Unfortunately she was still playing so I had to have another one, but it was nice to practise with her. I was a bit nervous but I liked it. It was a really good experience which helped me a bit today.

‘‘I’m a little bit surprised because Monica is a great player but I played so well.’’

Seles was generous in defeat.

‘‘You have to give so much credit to Daja because she served so well. But I made too many errors to stay competitive. It was one of those matches that didn’t feel comfortable from the first ball hit,’’ she said.

World number one Martina Hingis reasserted some of her authority with a commanding fourth round victory over Jelena Dokic.

Hingis moved up several levels from her previous tentative display against Iva Majoli to defeat Dokic 6-4 6-0 and cruise through to a quarter-final against Bedanova.

Like Seles, Hingis also took Bedanova under her wing as a youngster and knows how dangerous one of the women’s young guns could prove.

‘‘I know her very well,’’ said Hingis. ‘‘She has spent a few days in my home and we have practised together. She is a very talented youngster and she’s going to go a long way.’’

Not as far as Hingis, perhaps, who has now won all seven matches she has played under lights at Flushing Meadows.

Dokic, however, believes Hingis will struggle to go all the way to lift her first Grand Sland Slam title for more than two-and-a-half years.

The pair also practise together at the same Saddlebrook centre in Florida, so Dokic is ideally placed to gauge the strength of the top seed.

‘‘She has the game but at the moment she is struggling to beat three big-hitters in a row,’’ said Dokic. ‘‘She’s won Slams before though and she has a chance. You can’t count her out but even though she played well tonight she hasn’t been playing well generally and I think she’ll struggle.’’

Number three seed Lindsay Davenport struggled to overcome Russia’s Elena Likhovtseva after suffering a recurrence of a right knee injury in the second set.

She eventually triumphed 6-3 0-6 6-3 and then struck a blow for the tennis-paying public.

‘‘If ever you go to another sporting event whenever there’s a time-out or break in the action they’re doing something to entertain the fans,’’ said Davenport. ‘‘A lot of times people get bored or they want something to do.

‘‘Try something different, try to make it more exciting, just try and keep everybody entertained if it’s a good match, a bad match or whatever.’’

Belgian sixth seed Justine Henin must be fed up of the Williams sisters. Venus beat her in the Wimbledon final and today Serena, the 1999 champion and number 10 seed, listened to tips from her big sister to triumph 7-5 6-0.

Serena is now planning revenge against Davenport in what promises to be a big-hitting quarter-final. Williams, who lost to her fellow-American at the same stage last year, then explained why she enjoyed being a role model.

‘‘A lot of young black people look up to me and Venus and Marion Jones and other prominent athletes,’’ said Williams. ‘‘But I don’t feel pressure.

"I am a role model but I’m not doing things I don’t want kids to see me doing. Hopefully kids can learn from me just to have fun and live a good life.’’