How to prove this theorem (about general topology)?
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
152465
Find the intersection of all $T_2$ topologies on an infinite set $X$
106434
Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
133413
Proof of paracompactness of CW-complexes (J. Lee, Introduction to Topological Manifolds)
55484
Proving that the map from a topological space to a fiber bundle is open.
109570
How to show that the set of points of continuity is a $G_{\delta}$
79213
Proof about a Topological space being arc connect
122821
Is the following proof valid? About the closure of a subgroup, of a topological group, being again a subgroup
39010
Metrization of the cofinite topology
138825
The strong topology on $U(\mathcal H)$ is metrisable
4196
A valid proof for the invariance of domain theorem?
85870
Show this set is a base for some topology on $\mathbb{Z}$
76428
Exercise $2.1.1$ - Differential Topology by Guillemin and Pollack
122352
Topologies in a Riemannian Manifold
83665
Prove a assertion concerning Lebesgue space
44194
How to show that the unit sphere is a topological manifold?