Nick Clegg welcomed police action over Twitter abuse after a man was arrested on suspicion of harassment after threats were aimed at a feminist campaigner on the social networking site.
It comes after Caroline Criado Perez faced a deluge of threats on Twitter over the course of more than a day after she successfully campaigned for a woman's picture to be put on a new bank note.
The Deputy Prime Minister said: "What is unacceptable offline is unacceptable online."
He added that he had "probably" received lots of abuse on Twitter.
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Andrew Nay smashed into a family's car with his 4x4 during a road rage chase leaving two young sisters paralysed, a court heard.
Susan Whiting was attacked with a blunt object at the couple's bungalow, wrapped in a shower curtain, and hidden under a bed.
Teenager TJ Khayatan carried out the prank at the San Francisco Museum of Modern Art - and later posted the results on Twitter.