Noun
toplessness (uncountable)
The state of being topless, the state of not covering one's torso with garments.
She soon discovered that the customers preferred toplessness to cheaper drinks.
New Burlesque focuses on dancing, costumes and entertainment (which may include comedy and singing) and generally eschews full nudity or toplessness. Source: Internet
In a few Western countries female toplessness at a beach is acceptable, although it may not be acceptable in the town center. Source: Internet