I have 3 spaces A, B, C.
A is compact, the other 2 are not.
A and B are NOT homeomorphic, neither are A & C.
Suppose I can construct a continuous bijection a: C-->B & another b:B-->A.
How can I use this information to decide whether a is a homeomorphism?
Or is this NOT enough info?
If that is the case, I can tell you a bit more about the specific spaces I'm dealing with...
Many thanks in advance x