English

On locally extremal functions on connected spaces

General Topology 2008-11-12 v1 Metric Geometry

Abstract

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

Keywords

Cite

@article{arxiv.0811.1771,
  title  = {On locally extremal functions on connected spaces},
  author = {T. Banakh and M. Vovk and M. R. Wojcik},
  journal= {arXiv preprint arXiv:0811.1771},
  year   = {2008}
}

Comments

5 pages

R2 v1 2026-06-21T11:40:30.622Z