What does it REALLY mean for a metric space to be compact?
25752
What should be the intuition when working with compactness?
18040
Show that a compact metric space is bounded
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.
156304
Prob 12, Sec 26 in Munkres' TOPOLOGY, 2nd ed: How to show that the domain of a perfect map is compact if its range is compact?
27517
Isometry in compact metric spaces
47810
$C(X)$ is separable when $X$ is compact?
481
Can compact sets completey determine a topology?
151984
Proving the existence of a metric space
127173
Closed subset of compact set is compact
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
125233
Why is an open interval not a compact set?
134601
whether they are complete metric space
124959
Does weak compactness imply boundedness in a normed vector space (not necessarily complete)?
58948
If $A$ is compact, is then $f(A)$ compact?
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
143484
A separable locally compact metric space is compact iff all of its homeomorphic metric spaces are bounded