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2008-05-18T20:09:31Z

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Vipul: New page: ==Statement== # Suppose $f:M \to N$ is a continuous map between differential manifolds. Then, there exists a smooth map $f':M \to N$ such that $f'$
2008-02-02T02:17:12Z

New page: ==Statement== # Suppose <math>f:M \to N</math> is a continuous map between differential manifolds. Then, there exists a smooth map <math>f':M \to N</math> such that <math>f'</...

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==Statement==

# Suppose <math>f:M \to N</math> is a [[continuous map]] between [[differential manifold]]s. Then, there exists a [[smooth map]] <math>f':M \to N</math> such that <math>f'</math> is homotopy-equivalent to <math>f</math>
# Suppose <math>F:M \times I \to N</math> is a homotopy between smooth maps <math>f_0:M \to N</math> and <math>f_1:M \to N</math>. Then, there exists a homotopy <math>F':M \times I \to N</math> from <math>f_0</math> to <math>f_1</math> that is ''smooth'' as a map from <math>M \times I</math> to <math>N</math>.