On locally extremal functions on connected spaces

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We construct an example of a real-valued continuous non-constant function $f$ defined on a connected complete metric space $X$ such that every point of $X$ is a point of local minimum or local maximum for $f$. The space $X$ is connected but fails to be separably connected.
5 pages

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General Topology, Metric Geometry, 54D05; 54C30

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http://salesiana.dossiersoluciones.com/handle/123456789/173882

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0811.1771
 http://arxiv.org/abs/0811.1771

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arXiv