The main aim of this paper is to give a positive answer to a question of Behrends, Geschke and Natkaniec regarding the existence of a connected metric space and a non-constant real-valued continuous function on it for which every point is a local extremum. Moreover we show that real-valued continuous functions on connected spaces such that every family of pairwise disjoint non-empty open sets is of size < |R| are constant provided that every point is a local extremum.

On metric spaces and local extrema

FEDELI, Alessandro;
2009-01-01

Abstract

The main aim of this paper is to give a positive answer to a question of Behrends, Geschke and Natkaniec regarding the existence of a connected metric space and a non-constant real-valued continuous function on it for which every point is a local extremum. Moreover we show that real-valued continuous functions on connected spaces such that every family of pairwise disjoint non-empty open sets is of size < |R| are constant provided that every point is a local extremum.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/20292
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