# What is a non-topological manifold (if such a thing exists)?

So in my wikipedia readings, I have often stumbled across mentions of topological manifolds. I thought a manifold intrinsically had to be topological, either explicitly or implicitly like in a metric space. I don't even know how to conceptualise a non-topological manifold. Is this just wikipedia being weird, or are non-toplogical manifolds a thing, and if they are, what are they? Are there any examples I can see? And do they generalise topological manifolds, or are they their own thing?

• I see no reason why manifolds couldn't be based on Cech closure spaces or other generalized topological structures, although I doubt much of interest would arise from such things (by the way, saying this guarantees the opposite). However, the answer by @Arnaud Mortier is the real reason. Aug 11, 2018 at 11:27

If you were to write "let $X$ be a manifold", the reader would possibly wonder what class of manifolds you are considering.