A homomorphism between topological groups is continuous if it is continuous at one element
57468
Continuous homorphisms between topological groups.
57642
Uniform Continuity implies Continuity
103717
Topological Property of the Set of Integers
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
46970
If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism.
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
33140
Two non-homeomorphic spaces with continuous bijective functions in both directions
18343
Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$
23728
Does a continuous and 1-1 function map Borel sets to Borel sets?
135661
Weakly continuous operators are continuous
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
111246
product of two continuous proper maps
46287
Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
58484
Is the topological product $\Pi \{G_\alpha: \alpha < \kappa\} $ a topological group?
69652
Help understanding proof of every topological group is regular
116732
Proving that a continuous map is surjective
113498
Example of topological spaces where sequential continuity does not imply continuity