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Shyloh Mugler Curet’s home, a Bronx apartment she shares with her 83-year-old grandmother, has not always felt like one.

She faced rejection from her family when she came out as gay. “Keep it to yourself,” some relatives told her.

Several years ago, Ms. Mugler Curet, a transgender woman, was robbed and sexually assaulted as she was returning home. It rattled her so deeply she felt she had to leave the city for a time, seeking safety in Florida and Massachusetts.

“That’s what you get,” she told herself, her grandmother’s chilling warnings echoing in her head.

She eventually did return to the Bronx, and soon found a haven, a space safe enough to grow more comfortable with herself: Destination Tomorrow, a center that has been serving the borough’s gay, lesbian, bisexual and transgender community for nearly a year.