$f:A \backslash U\to B \backslash f(U)$ is also homeomorphic?
134070
$g$ a restriction of a homeomorphic function $f$, $g$ also homeomorphic?
33140
Two non-homeomorphic spaces with continuous bijective functions in both directions
65034
Are continuous self-bijections of connected spaces homeomorphisms?
53168
Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
27629
How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
157987
Can a space $X$ be homeomorphic to its twofold product with itself, $X \times X$?
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
93776
Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
26197
$B^n/S^{n-1}$ is homeomorphic to $S^n$
77563
Homeomorphism between spaces equipped with cofinite topologies
72642
Continuous bijection from $(a,b) \to S^1$?
115347
Showing that the fiber of a morphism of schemes over a point is homeomorphic to the preimage
32765
$\mathbb{C}\mathbb{P}^1$ is homeomorphic to $S^2$
14830
A transformation of F[x]
46563
Show that the quotient space is homeomorphic to the n-disc
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?