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Results tagged with gn.general-topology
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user 22989
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
8
votes
Accepted
Universal maps between topological spaces
This seems to be answered negatively in "On the composition and products of universal mappings" by W. Holsztyński (Fundamenta Mathematicae 64(2) (1969), 181-188).
I've not looked at the proof or real …
- 35.2k
8
votes
Accepted
Minimal Hausdorffness reversed
Yes.
Let $\tau$ be a non-Hausdorff topology on a set $X$.
Suppose first that $\tau$ is not $T_1$, so there are two points $a,b\in X$ such that every open neighbourhood of $a$ contains $b$. Then $\t …
- 35.2k
15
votes
Accepted
Which spaces have the (weak) homotopy type of compact Hausdorff spaces?
Expanding on my comment, if there are measurable cardinals then it follows from the results of
A. Przeździecki, Measurable cardinals and fundamental groups of compact spaces.
Fund. Math. 192 (2006), …
- 35.2k
5
votes
Free and cellular G-action implies free G-complex?
If $G$ acts freely on a CW-complex, permuting the cells, then the stabilizer of a cell must be finite (and therefore trivial, as pointed out in the question).
This can be shown by induction on the di …
- 35.2k
8
votes
Is an open subset of a rigid space rigid?
The answers to (1) and (2) are "no" in general for metrizable spaces.
Let $C$ be a connected compact metric space with more than one point, with the property that the only continuous self-maps of $C$ …
- 35.2k