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Results tagged with at.algebraic-topology
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user 31951
Homotopy theory, homological algebra, algebraic treatments of manifolds.
5
votes
2
answers
640
views
Homotopy equivalences preserving structure
Suppose I have $X=X_1\cup X_2\cup…\cup X_n$ and $f:X \to Y$ where $Y$ has a similar decomposition.
Suppose I know that
$f | X_{i_1}\cap…\cap X_{i_r} \to Y_{i_1}\cap…\cap Y_{i_r}$ is a homotopy equiv …
- 51
35
votes
Accepted
The role of ANR in modern topology
Another reason you might not see the word ANR these days is that compact finite-dimensional spaces are ANRs if and only if they are locally contractible. Thus, "finite-dimensional and local contractib …