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Results tagged with gn.general-topology
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user 6074
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
2
votes
Uniform spaces as condensed sets
Here is an essentially tautological answer. The notion of uniformity makes sense also for condensed sets -- it is a condensed set $X$ together with certain subsets $U\subset X\times X$ termed entourag …
- 21.3k
9
votes
Accepted
Countable sum $\bigoplus_{n=0}^\infty\mathbb Z_p$ as a topological group
The sum $M=\bigoplus_{\mathbb N} \mathbb Z_p$ is not first-countable, but it is Cauchy complete. More precisely, $M$ maps isomorphically to $\varprojlim_{U\subset M} M/U$ where $U$ runs over open subg …
- 21.3k
7
votes
Structure of a profinite group as a condensed set with an action of an open subgroup
Yes, that is true. I'm not sure I'm explaining the step that's confusing you, but you are asking about a special case of the statement that the functor $S\mapsto\underline{S}$ from profinite sets to c …
- 21.3k