Proving injective continuous function is homeomorphism
34699
A continuous bijection from a compact space to a $T_2$ space is always a homeomorphism
148187
Question regarding one-point compactification and homeomorphisms
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
29154
$f$ is continuous and open implies $f$ injective
2093
If $f$ is continuous then $G$ is homeomorphic to $X$.
32359
Inner product of two continuous maps is continuous
143174
property of continuous function
72044
prove $x \mapsto x^2$ is continuous
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
31266
Proof of "the continuous image of a connected set is connected"
117502
Proving that a certain continuous function is surjective.
99179
Continuous function with compact domain has continuous inverse
91736
Explicit homeomorphism between open and closed rational intervals?
35953
Prove that a function is not injective
84301
Showing that some Function on the Unit Disc is injective