The product metric space of two compact metric spaces is compact
29303
Cartesian product of compact sets is compact
95783
Fixed points of contractions in metric spaces
153573
Counter Example for the union of any number of compact sets is compact in T2-spaces
146146
Proof that a closed subset of a compact space is a compact space
19566
Continuous images of compact sets are compact
35652
Every compact metric space is complete
92005
Existence of compact/complete metric on countable set
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
140124
The distance function on a metric space
90628
The metric spaces are Tychonoff spaces
154978
Some equivalent formulations of compactness of a metric space
128897
Bounded sequence in a metric space
9775
Metric on Cartesian Product
48557
Product of connected spaces
151984
Proving the existence of a metric space
11383
Disjoint compact sets in a Hausdorff space can be separated
14509
Contraction Map on Compact Normed Space has a Fixed Point