"Closed subsets of compact space are compact" with an alternative definition of covering.
106534
"Closed subsets of compact space are compact" with an alternative definition of covering
133152
(X,d) be a compact metric space. For every open cover, show there exists ε > 0 such that ∀𝑥 ∈ X, B(x,ε) is contained in some member of the cover.
153256
Compact topological space with closed graph implies continuity
29744
Compactness and axiomatisability
99645
Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
65180
A compact Hausdorff space that is not metrizable
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
106957
Compact sets are closed?
65976
in a topological space only finite subsets are compact sets
86309
Whether the set $A$ is a compact subset of $M_3(\Bbb R)$.
8015
Compact set plus a closed set is a closed set
66334
How is every subset of the set of reals with the finite complement topology compact?
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
19566
Continuous images of compact sets are compact
51914
Show that $S$ is compact.
94485
Limit point compactness implies compactness.
22131
Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.