Show that a closed graph and compact codomain implies continuity.
49703
Analogue of closed graph theorem
136583
Infimum is a continuous function, compact set
15487
Continuous function from a connected set?
140929
Increasing, continuous function implies connectivity and viceversa.
84512
The preimage of continuous function on a closed set is closed.
90152
Continuous with compact support implies uniform continuity
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.
154572
Continuity of a function at an isolated point
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
7402
Showing a compact metric space has a countable dense subset
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
154559
For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
43376
If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved
102048
Closure of a compact set in Regular space $ X $
76607
Show that exists a continuous function in $E$ that is not bounded
46834
show that a distance function is continuous
143951
Can we determine uniform continuity from graphs?