distance between two non-empty subsets, closed and compact, of a metric space
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
123061
$X$ metric separable then $C(X)$ separable
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
72950
Book recommendation for Metric Spaces
8015
Compact set plus a closed set is a closed set
36237
Closed set mapped to itself in a compact Hausdorff space
28391
Prove the compactness of a set B
36566
Equivalence classes and metric spaces
50677
Is this metric space incomplete?
121135
Why don't we use closed covers to define compactness of metric space?
6415
Distance function is continuous in topology induced by the metric
135315
Proving whether a function on the set of real sequences is a metric
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
88185
Proof that a subspace $A$ of a complete metric space $X$ is complete iff $A$ is closed
18040
Show that a compact metric space is bounded