Suppose M and N are smooth manifold with M connected, and F:M->N is a smooth map and its pushforward is zero map for each p in M. Show that F is a constant map.(adsbygoogle = window.adsbygoogle || []).push({});

I just remember from topology, the only continuous functions from connected space to {0,1} are constant functions. With this be useful in solving the problem?

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# Smooth manifold and constant map

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