Timeline for Does the CGWH-fication change the (weak) homotopy type?
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| Jun 17, 2015 at 15:21 | comment | added | Eric Wofsey | @Klaus: It's a theorem of McCord; here's the original reference. One version of the statement is as follows. Let $X$ be a simplicial complex, and let $Y$ be the quotient of $X$ obtained by collapsing the interior of each simplex of $X$ to a point. Then the quotient map $X\to Y$ is a weak equivalence. When $X$ is a finite simplicial complex, of course, this $Y$ is a finite space. | |
| Jun 17, 2015 at 14:19 | comment | added | Klaus | "However, finite spaces can have the weak homotopy type of any finite CW-complex!" This is impressive. Do you have a reference for this fact? | |
| Jun 17, 2015 at 14:09 | history | answered | Eric Wofsey | CC BY-SA 3.0 |