f: R to R. For all open subset U of R, we have f(U) is open, too. Prove that: f is monotonic.
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Originally Posted by felixmcgrady f: R to R. For all open subset U of R, we have f(U) is open, too. Prove that: f is monotonic. If is not monotonic, it will have a local extremum at some point . What can you say about an open ball around ?
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