Characterization of continuity via closed.
34699
A continuous bijection from a compact space to a $T_2$ space is always a homeomorphism
54600
Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?
108734
$T$ is continuous if and only if $\ker T$ is closed
81933
Topological spaces in which a set is the support of a continuous function iff it is the closure of a open set.
18222
Set of continuity points of a real function
42494
The boundary is a closed set
68994
Countable closed sets
78117
Closed property of nonempty finite set
90619
For closed subsets $A,B \subseteq X$ with $X = A \cup B$ show that $f \colon X \to Y$ is continuous iff $f|_A$ and $f|_B$ are continuous.
97316
Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X
151923
$F$ closed and connected then...
27661
The closed graph theorem in topology
156996
Do there exist general conditions under which we can conclude that continuity on a topological space is detected by $\mathbb{R}$?
158523
Topology: Proof that a finitely generated cone is closed
35573
A closed ball in a metric space is a closed set
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
14896
Prove: the set of zeros of a continuous function is closed.