$f:X\rightarrow Y$, with $Y$ compact, is continuous $\Rightarrow$ its graph is closed
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
28637
Proving continuous image of compact sets are compact
29582
Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
91682
Graph of a continuous function is closed
136011
Must $f$ be continuous?
15487
Continuous function from a connected set?
110744
How to prove that a compact set in a Hausdorff topological space is closed?
139612
Follow-up regarding right-continuous $f:\mathbb{R} \to\mathbb{R}$ is Borel measurable
8015
Compact set plus a closed set is a closed set
54600
Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?
90152
Continuous with compact support implies uniform continuity
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
41690
Products of Continuous functions: Topology
27661
The closed graph theorem in topology
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes