It is not a closet.
It is a room.
I do not care if you do not have a bath, you [i]bathe[/i] in there.
Showering is a form of Bathing yourself, is it not?
If it isn't, i don't care.
It's a bathroom.
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Ever been in really old houses before? The bathrooms were tiny. Only big enough for the toilet and a wall hung sink. The room was called the water closet BECAUSE that was the location of 'the water closet'. The toilet.