How do you define 'gymnasium'?

Here is how I define 'gymnasium':
NOUN
1) in ancient Greece, a place where students were trained naked in physical exercises
2) in modern times, a building for physical exercises equipped with various apparatus for strength training and aerobics and also housing other areas such as locker rooms, shower stalls, offices, classrooms, etc.
3) an auditorium for indoor sports such as basketball, volleyball, wrestling, gymnastics, etc. that is usually on the campus of an educational institution