On locally extremal functions on connected spaces

Details On locally extremal functions on connected spaces On locally extremal functions on connected spaces

2008-11-11

arxiv.org/abs/0811.1771v1

Mathematics

General Topology

5 pages

Scientific paper

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.

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