Show that one point compactification of $\Bbb Q$ is not Hausdorff .
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
98756
Unit ball in $C[0,1]$ not sequentially compact
4518
How would one go about proving that the rationals are not the countable intersection of open sets?
106606
How to prove that compact subspaces of the Sorgenfrey line are countable?
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
151637
How do we prove that this set is not manifold?
69046
Proof of $\mathbb{Q}$ is not cyclic
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
125668
A proof that BS(1,2) is not polycyclic
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
128711
$(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
64375
Non-Metrizable Topological Spaces
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
72875
"Naturally occurring" non-Hausdorff spaces?
123208
Show that the Sorgenfrey line does not have a countable basis.