CLEVELAND - Donald Trump was the center of attention at a testy first Republican presidential debate on Thursday, drawing boos from the crowd and a rebuke from a rival when he refused to rule out an independent White House bid and bristled at questions about his attitudes toward women.With 10 Republicans vying for air time in the two-hour debate, the candidates at times turned on one another rather than direct their fire toward Democratic front-runner Hillary Clinton or President Barack Obama.But Senator Rand Paul of Kentucky was the only contender to directly take on Trump, challenging him after he kicked off the debate by refusing to pledge his support for the Republican nominee in the November 2016 election."I will not make the pledge at this time," said Trump, who for weeks has said he would not rule out an independent bid that would likely split the Republican vote and boost the chances of victory for Clinton or another Democrat.Trump's response drew boos from the crowd and a rebuke from Paul, who said Trump was keeping his options open to support Clinton, a veiled reference at his past friendship with both Clinton and her husband, Bill."He's already hedging his bets because he's used to buying politicians of all stripes," Paul said.Pressed by Fox News moderator Megyn Kelly about past derogatory comments he had made about women, including calling them "fat pigs," "dogs," and "slobs," Trump dismissed the question as "political correctness." He accused Kelly of not treating him well, drawing more boos from the audience."Honestly Megyn, if you don't like it, I'm sorry. I've been very nice to you although I could probably maybe not be based on the way you have treated me," Trump, whose base of support is overwhelmingly male, said to a mixture of boos and applause.The feisty tone suited Trump, a flamboyant billionaire who has been the center of campaign attention for weeks for his personal attacks on rivals and his scathing comments about Senator John McCain's war record and about Mexican immigrants.Trump kept it up in the debate, calling the Mexican government "much smarter, much sharper, much more cunning and they send the bad ones over."The sometimes combative nature of the debate made it difficult for more measured candidates like former Florida Governor Jeb Bush, who is No. 2 in the polls, and Wisconsin Governor Scott Walker to make an impact.Bush, Walker and the other top contenders largely steered clear of tangling with Trump, focusing on their records and the conservative policies they would pursue if elected.Bush did call Trump's rhetoric "divisive" and said "we're going to win when we unite people with an optimistic message."Trump has rocketed to the top of opinion polls amid the controversies, heightening anticipation for the debate against rivals Paul, Bush, Walker, Marco Rubio and five other Republican hopefuls. SIDE BY SIDEThe debate was the first chance for Republican voters to make a side-by-side comparison of the top 10 presidential contenders. It offered Trump a chance to prove he could go beyond his bomb-throwing rhetoric and offer some policy specifics.Republican strategists have argued that once Trump was on the debate stage, he would be exposed as a faux conservative. And when Trump seemed to defend a single-payer healthcare system, or mentioned Hillary Clinton attended his wedding, or spoke of giving donations to both parties, he seemed to play into their hands.Trump's rivals had to decide whether to directly confront him or to try to stay above the fray and look presidential. Paul, who has lagged in the opinion polls, decided to go on the offensive.In addition to challenging Trump on his potential independent run, Paul accused Trump of not realizing that Republicans opposed a single payer healthcare system. But Trump dismissed his attacks."You're having a hard time tonight," Trump said.New Jersey Governor Chris Christie belittled Paul's efforts in the Senate to curtail the government's electronic surveillance system, saying there should be more tools for tracking terrorists."When you're sitting in the subcommittee just blowing hot air about this, you can say things like that," Christie said.Trump took his own shot at Christie's native New Jersey. "I had the good sense to leave Atlantic City, which by the way, Caesar's just went bankrupt."Before the main event, seven candidates whose poll ratings did not qualify them for prime time took part in a separate daytime debate. Several challenged Trump's conservative credentials, noting he had changed positions on abortion, healthcare and other issues.But Carly Fiorina, a former business executive and the only woman in the Republican field, acknowledged Trump had tapped into a broad sense of frustration with Washington."Whatever your issue, your cause, the festering problem you hoped would be resolved, the political class has failed you. That's what Donald Trump has tapped into," said Fiorina, who was the runaway choice at more than 80 percent when Fox News asked viewers to tweet who they thought won the first debate.Shortly after the early debate, social media interest in Fiorina surpassed interest in Trump, according to Google analytics.