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 defined on a connected complete metric space such that every point of is a point of local minimum or local maximum for . The space is connected but fails to be separably connected.
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