Prove there exists farthest points in a compact set.
111119
Distance between any two points in a compact metric space
98609
Does pointwise equicontinuous and uniformly equicontinuous implies compactness?
146756
Convergence at infinitely many points in a compact set and convergence in the whole region
142779
How to show distance between boundary of an open set and a compact subset is positive?
66334
How is every subset of the set of reals with the finite complement topology compact?
146146
Proof that a closed subset of a compact space is a compact space
16826
prove that every infinite subset of compact set H has a limit point (Explanation)
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
79531
Distance between sets with one closed set and one compact set
481
Can compact sets completey determine a topology?
70106
diameter on a compact metric space
41408
Which of the following sets are compact:
103383
Let $\{K_i\}_{i=1}^{\infty}$ a decreasing sequence of compact and non-empty sets on $\mathbb{R}^n.$ Then $\cap_{i = 1}^{\infty} K_i \neq \emptyset.$
80180
Discrete and compact subset must be finite
58007
Proof: Show there is set of $n+1$ points in $\mathbb{R}^n$ such that distance between any two distinct points is $1$?
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
116542
Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]