Proving that a well-ordered set with the order topology is not homeomorphic to any initial segment of it
132298
How do you find the smallest of homeomorphic ordinals?
19297
Is the cofinite topology on an uncountable set first countable?
1508
How do I prove that a definition of an ordered pair does not satisfy the required property?
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
128118
Is the cofinite topology on a countable set first countable?
107076
Prove $S^1$ is not homeomorphic to $S^2$ using connectedness
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
46287
Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
91281
Proving the so-called "Well Ordering Principle"
102079
If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
99464
Proof Concerning Indexed family of Sets and Intervals
115173
The Cantor set is homeomorphic to infinite product of $\{0,1\}$ with itself - cylinder basis - and it topology
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
133820
The product topology on $\mathbb R_d\times \mathbb R$ vs. the dictionary order topology on $\mathbb R\times \mathbb R$
31266
Proof of "the continuous image of a connected set is connected"