$X$ be locally compact & $T_2$, then $\forall x\in U$ where $U$ is open,$\exists V$ open with compact closure $\ni x\in V\subset\overline{V}\subset U$
118765
A topological space is locally compact then here is an open base at each point has all of its set with compact closure
106957
Compact sets are closed?
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
41408
Which of the following sets are compact:
8015
Compact set plus a closed set is a closed set
39076
Contraction of compact sets
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
12293
Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
71829
Is closure of convex subset of $X$ is again a convex subset of $X$?
153256
Compact topological space with closed graph implies continuity
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
142459
Continuity of a Function in Terms of Closure and Interior
141642
Closure of a certain subset in a compact topological group
140570
Suppose $E\subseteq\mathbb{R}$ is closed and $K\subseteq\mathbb{R}$ is compact. Show that every open cover of $E\cap K$ has a finite subcover
102924
Normal space- equivalent condition: $\forall U, V$ - open $: U \cup V = X \ \ \ \exists F \subset U \ , G \subset V$ - closed $: F \cup G = X$
51914
Show that $S$ is compact.