Hi all, I have the following question. Are the following spaces homeomorphic in the real number space with absolute value topology? 1) [a,b) and (a,b] 2) (a,b) and (r,s)U(u,v) where r < s < u < v. For 1), I got that they are not homeomorphic because it fails the topological property that sequences in a set converges to a point in the set. As seen, a sequence could converge to a point a in [a,b), which is in the set, but is not contained in the set (a,b]. -Is this correct? For 2), I'm not really sure at all. I was wondering if I should try to create a function that maps (a,b) to (r,s)U(u,v) and show the properties for homeomorphisms under topological spaces but I can't find out a function.