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Will U.K. lawmaker's murder impact EU membership vote?

LONDON -- Speaking for her family, the sister of slain British parliamentarian Jo Cox told her country and the world that the violent attack would not quell her sister's spirit.

"For now, our family is broken, but we will mend over time and we will never let Jo leave our lives," Kim Leadbeater said. "She will live on through all the good people in the world."

The vicar of the local church in Birstall, near the city of Leeds, also spoke on behalf of the community.

"Jo was someone who went out of her way to help others," he said just half a mile from the spot where Cox was shot and stabbed to death after leaving an event in her constituency. "I regret to say I didn't know what she was like as girl, but she grew into a fervent advocate for the poor and the oppressed."

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Flowers surround a picture of Jo Cox during a vigil in Parliament Square, June 16, 2016 in London, United Kingdom. Getty

CBS News correspondent Elizabeth Palmer says the condolences flooding in have shown just how much Cox was admired and respected, and how deeply traumatic her murder has been for the community and Britain as a whole.

Accused killer of U.K. lawmaker appears in court 01:34

She was killed on Thursday, and sole suspect Thomas Mair, 52, was arrested almost immediately nearby.

His family has said he has a history of mental problems, and when Mair was asked to state his name in court on Saturday, he responded bizarrely, blurting out, "death to traitors -- freedom for Britain."

Link between U.K. politician's murder and U.S. neo-Nazi group 02:34

The Southern Poverty Law Center, an American civil rights organization that monitors hate groups, said Mair was a supporter of the National Alliance, "the most dangerous and violent neo-Nazi group in the United States for decades."

The Center said Mair had sought materials on firearms, bomb-making and survivalist skills.

In Britain, many saw the slaying as an attack on the things Jo Cox stood for as a Member of Parliament -- especially her passionate advocacy for the rights of refugees.

Britain is in the middle of a bitter fight over whether to abandon its membership in the European Union, and immigration is central to the debate.

After Cox's murder, both sides paused their sometimes rowdy campaigning for three days, out of respect.

But now it's resumed. Cox's position, for Britain to remain in Europe with its open borders, appears to have retaken a slight lead in the polls, and is gaining.

Mair was to be back in court Monday for a bail hearing.

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