On locally extremal functions on connected spaces

2008/11/11 by T. Banakh, Тарас Банах, Banakh, T. +5 · 1 citation
Mathematics · #54C30 #54D05 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Metric Geometry (math.MG) #math.GN #math.MG #msc:54C30 #msc:54D05

paper · pdf · doi:10.48550/arxiv.0811.1771

5 pages

arxiv created 2008/11/11 · openalex publication_date 2008/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Nonseparably connected complete metric spaces

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