Distance between compact sets in a metric space.
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
39076
Contraction of compact sets
36566
Equivalence classes and metric spaces
151832
uniformly convergence on compact metric space
11383
Disjoint compact sets in a Hausdorff space can be separated
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
79531
Distance between sets with one closed set and one compact set
28637
Proving continuous image of compact sets are compact
35156
Constructing a choice function in a complete & separable metric space
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
132641
Proving that Euclidean Space is a complete metric space
66550
Cardinality of separable metric spaces
49563
Cauchy nets in a metric space
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.
83159
Defining a metric space
28391
Prove the compactness of a set B
6793
A linearly independent set about approximate units