Proving Non-metrizable spaces
106298
Prove that some topology is not metrizable
70413
A vector space over $R$ is not a countable union of proper subspaces
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
64840
A Banach space that is not a Hilbert space
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
70049
Irreducible topological spaces and irreducible Hausdorff space
151984
Proving the existence of a metric space
138825
The strong topology on $U(\mathcal H)$ is metrisable
45249
Pseudocompactness does not imply compactness
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
31002
Proving that the unit ball in $\ell^2(\mathbb{N})$ is non-compact
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
128266
Dual Spaces and Natural maps
66895
A condition for the image of a metrizable space to be metrizable
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
33207
Bases having countable subfamilies which are bases in second countable space