[gjulianm]

Doesn't that add to the point that sometimes literal definitions are better than symbolic? Either you have a symbol that says "this is a neighbourhood" or you have the symbolic definition of neighbourhood (which is missing in my symbolic definition of the space, btw, I just noticed) and then you force the reader to identify those symbols and say "oh, this is a neighbourhood". The former is the same issue as in English, and the latter adds unnecessary complexity (no people reading about Hausdorff spaces will be unfamiliar with the concept of a neighbourhood of a point).