A Brooklyn man has been arrested in connection with the rape of a 23-year-old woman inside her Williamsburg apartment building last week, police said.

Laye Kaba, 31, was charged by police with rape, stalking, sex abuse, burglary, strangulation, unlawful imprisonment and menacing.

Bail was set at $125,000 bond during a court appearance in Brooklyn Friday, officials at the Brooklyn district attorney's office said.

According to police, the woman was followed into her apartment building at about 5:45 a.m. Saturday, Nov. 17, and raped her.

It wasn't immediately clear if the rapist knew the victim.