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Results tagged with at.algebraic-topology
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user 31951
Homotopy theory, homological algebra, algebraic treatments of manifolds.
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 …
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