Showing that a closed unit ball is not compact
9545
Closed ball is not compact
36237
Closed set mapped to itself in a compact Hausdorff space
110744
How to prove that a compact set in a Hausdorff topological space is closed?
147914
Closed image of locally compact space
34173
Banach spaces and their unit sphere
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
99678
Is a sphere a closed set?
84921
Fitting an infinite collection of balls in an infinite dimensional unit ball
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
39842
Limit point Compactness does not imply compactness counter-example
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
37654
Topology: Example of a compact set but its closure not compact
43248
Closure of a Ball is Contained in Closed Ball (usual metric)