A question about compact sets: how to prove $g$ must be an isometry
119247
Let $(M,d)$ be a compact metric space and $f:M \to M$ such that $d(f(x),f(y)) \ge d(x,y) , \forall x,y \in M$ , then $f$ is isometry?
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
109570
How to show that the set of points of continuity is a $G_{\delta}$
48783
Prove that the sum of two compact sets in $\mathbb R^n$ is compact.
47031
Isometric to Dual implies Hilbertable?
106957
Compact sets are closed?
42084
Set of points of continuity are $G_{\delta}$
46116
Proof of the First Isomorphism Theorem for Groups
41408
Which of the following sets are compact:
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
11383
Disjoint compact sets in a Hausdorff space can be separated
11762
Compactness of a Sphere
106178
Question of an isomorphism of $\epsilon_ 0$ and a subset of the rationals.
104855
Prove that $N \subset Z(G)$
8015
Compact set plus a closed set is a closed set