Poland's Agnieszka Radwanska eased into the quarterfinals when she beat Hungary's Greta Arn of Hungary 6-3, 6-4.
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In other matches, top seed Maria Sharapova suffered a shock 6-2 7-5 defeat by Hungarian veteran Greta Arn.
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Clijsters had to overcome a wobble in the second set to beat Greta Arn 6-0 7-5 and book her place in round two.
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The Londoner also came through qualifying at the Pan Pacific Open in Tokyo in September, before losing in the first round to Hungary's Greta Arn.
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Paraguay's Rossana Neffa-De Los Rios was another comeback winner against German Greta Arn, amd her 0-6 7-6 7-6 won sets up a clash with sixth seed Alexandra Stevenson.
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