Let R denote the real line and R^2 the real plane.
How do I show that R^2 and R^2 - {(0,0)} are not homeomorphic? I don't even know where to start since I cannot think of a topological property that is in one but not in the other. Can anyone give me a clue on what that property is?
A...
I found this interesting exercise on a topology book I'm reading, but I don't have a clue what to do.
Show that there is no sequence {g_n} of continuous functions from R to R such that the sequence {(g_n)(x)} is bounded iff x is rational (where R = set of real numbers).