Is a self-embedding of a compact metric space automatically an isometry?
7081
isometry $f:X\to X$ is onto if $X$ is compact
111236
Is there a reference for compact imbedding of Hölder space?
74657
Can this intuition give a proof that an isometry $f:X \to X$ is surjective for compact metric space $X$?
16060
Showing this metric space is complete
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
9775
Metric on Cartesian Product
95831
Compactness and sequential compactness in metric spaces
133938
Connectedness of the Hausdorff distance.
135315
Proving whether a function on the set of real sequences is a metric
45581
Is the distance function in a metric space (uniformly) continuous?
1756
1-point compactification and embedding
90628
The metric spaces are Tychonoff spaces
60868
Interplay of Hausdorff metric and Lebesgue measure
84004
Prove there is no contraction mapping from compact metric space onto itself
39763
Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure
31686
Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set
3751
Proving a distance between molecules defines a metric space.