Hello, I have been given a homework problem and I don't want any help on solving the problem, (I'm not even going to post the problem - I want to figure it out myself), I only want to understand what the problem is asking. (That's why I've posted in this section rather than the homework section. This is just a general concept question.) Essentially, there are pictures of two triangles (I'm gonna draw a pic and link to the pic) http://i.imgur.com/VKpet.jpg The question begins "consider the following identification spaces of a triangle" So I know that identification space means quotient space. But I have a difficult time understand what this quotient space here is supposed to be. So this is my understanding of a quotient space: You have some topological space, X, and an equivalence relation ~ on it. The quotient space, A, is then the set of equivalence classes on X. Now, if you have a surjective mapping from X on to A and you define sets in A as being open if their preimage in X is open, then this defines a topology on A, and we call this the quotient topology. So what is the equivalence relation ~ in these diagrams? Does it mean that the interior points are all just equivalent to themselves (they don't change) but that the points on each edge are an equivalence class? Also, I understand how a triangle or polygon in general can have an orientation. For example, the triangle on the left has an orientation but the one on the right does not appear to be orientable. But what does this orientation have to do with the equivalence relation ~?