this is a tank top.

This is a tank top (underneath a used shirt from the Gap that I have had now for several months).

I have several of them: pink, white, black, blue, stripes, maroon... well, ok, more than several of them.  They keep me warm, are helpful if your shirt is a bit see-through, and they provide a few more inches beneath your shirt so that it is ok to wear it in public.