TITLE: What does a space mean?
QUESTION [11 upvotes]: In Wikipedia, they say that  a space is a set with some added structure. But what do they mean by "with some added structure"?

REPLY [2 votes]: There is a formal definition of structure, see here. In this definition, structure is clearly distinguished from property and from something else called stuff. This formalism may look highbrow, but on closer inspection it's not that complicated and makes a lot of sense.