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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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) …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar