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Results tagged with gn.general-topology
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user 4008
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
17
votes
Accepted
Is the Characteristic of a Field Detectable from the Topology of a Topological Vector Space?
I think all non-archimedean locally compact fields are homeomorphic: Their rings of integers are compact, metric and totally disconnected and hence are all homeomorphic (to the Cantor set). The same i …
- 22.6k
15
votes
Confusion over a point in basic category theory
If what you mean by "the category of topological spaces" is the category whose objects are pairs $(S,T)$
where $S$ is a set and $T$ is a topology on $S$ and by topological space you mean a pair $(S,T …
- 22.6k
11
votes
Accepted
Topological dimension versus cohomological dimension
Well, I think it depends on which dimension you mean and which cohomology. The best fit I think is covering dimension and Čech cohomology. The Čech cohomological dimension is indeed bounded (more or l …
- 22.6k
8
votes
On the cohomology of a finite covering map
There is a precise relation at the level of complexes: $C^\ast(X,\mathbb Z)$ is a $G$-complex and as such it is perfect (that is quasi-isomorphic to a finite complex consisting of projective modules) …
- 22.6k