Compact Metric Spaces & Triangle Inequality Theorem
53812
Metric is continuous function
9268
Proving that the Union of Two Compact Sets is Compact
60868
Interplay of Hausdorff metric and Lebesgue measure
17067
To prove that $(\mathbb{P(N)},d)$ is a metric space
35573
A closed ball in a metric space is a closed set
93599
General Proof for the triangle inequality
146485
Prove that the product space is a metric space.
152493
Is an expanding map on a compact metric space continuous?
140124
The distance function on a metric space
49374
Closure of a subset in a metric space
123061
$X$ metric separable then $C(X)$ separable
157753
Show that any set in a metric space can be written as the intersection of open sets
23845
How to prove the continuity of the metric function?
19566
Continuous images of compact sets are compact
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent