Motivation for the definition of continuous maps on topological spaces
67948
Why are continuous functions the "right" morphisms between topological spaces?
78344
Nonconstant linear functional on a topological vector space is an open mapping
158349
Prove the map sending a matrix to it's inverse is continuous.
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
153952
A map between metric spaces preserving convergent sequences is continuous
118851
$X$ be a Hausdorff topological space , let $f:X \to X$ be a continuous map such that $f\circ f=f$ , then is $f(X)$ is closed in $X$ ?
116663
If f is a continuous map from X to Y with X limit point compact, does it follow that f(X) is limit point compact?
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
46788
Compact open topology on space of continuous maps from a discrete space is a product
156996
Do there exist general conditions under which we can conclude that continuity on a topological space is detected by $\mathbb{R}$?
133422
How to prove the continuity of an induced map; $g_* : C(X, Y) \rightarrow C(X, R)$, induced from the map $g \in C(Y, R)$, endowed with fine topology.
41690
Products of Continuous functions: Topology
77563
Homeomorphism between spaces equipped with cofinite topologies
64487
Continuous function and dense set
17607
Open maps which are not continuous
72190
Topological proof on discrete topology where $X$ is infinite