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Results tagged with gn.general-topology
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user 1874
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
6
votes
1
answer
707
views
is this map a closed inclusion?
I apologize in advance if this question is too technical. I haven't found a reference in the literature yet, and it seems difficult enough that perhaps it has not been answered.
Let $A$, $B$, and $C$ …
- 1,207
25
votes
2
answers
2k
views
CW complexes and paracompactness
It seems like when we assume "niceness" in homotopy theory we assume that $X$ has the homotopy type of a CW complex, and in fiber bundle theory we assume that $X$ is paracompact. How do these two inte …
- 981
8
votes
2
answers
863
views
Is the mapping cylinder of a Serre fibration also a Serre fibration?
If we have a Serre fibration $p: E \rightarrow B$ with fiber of homotopy type $S^{k-1}$, then we can create a fibration with contractible fiber by first taking the mapping cylinder $M_p$ of $p$ to get …
- 9,263
11
votes
5
answers
1k
views
Confusion over a point in basic category theory
"Let Top be the category of topological spaces." If I see a definition like this, in which homeomorphic (isomorphic in the category) spaces are not identified together, then for each given topological …
- 65.4k