Synonyms for Singlet:

n.

cup, shin pad, box, jock, jersey, leotard, kit, jockstrap, athletic supporter, shin guard. corset, crop top, boob tube, dress shirt, dickey, kameez, kaftan, halter, blouse, kurta. artifact (noun)
undershirt, vest.
singlet (noun)
undershirt, vest.

Other synonyms:

Other relevant words:
box, jersey, cup, corset, jock, kit, dickey, kaftan, blouse, jockstrap, kurta, kameez, halter, leotard.