On locally extremal functions on connected spaces

Abstract

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

Cited by in corpus (2)

• A Nonseparably Connected Metric Space as a Dense Connected Graph
• Nonseparably connected complete metric spaces