Male supporting generally empty exercise venue (3)

I believe the answer is:
gym
'exercise venue' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'male supporting generally empty' is the wordplay.
'male' becomes 'm' (common abbreviation).
'supporting' says to put letters next to each other (in a down clue, some letters go below others).
'empty' suggests removing the centre.
'generally' with its middle taken out is 'gy'.
'm' put after 'gy' is 'GYM'.
Can you help me to learn more?
(Other definitions for gym that I've seen before include "Place to get fit" , "Training room" , "Lesson" , "Physical education" , "Area for physical exercise in short" .)
