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If $X,Y$ are CW-complex and a cellular map $f$ from $X$ to $Y$, is it necessarily that ${M_f}$ is a CW-complex?

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This would be appropriate for math.stackexchange.com, as it's a homework-type problem. – Ryan Budney Sep 2 2011 at 6:56

closed as too localized by Ryan Budney, Gjergji Zaimi, Daniel Litt, Torsten Ekedahl, Daniel Moskovich Sep 2 2011 at 8:56

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