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. © 2009 Elsevier B.V. All rights reserved.
On metric spaces and local extrema / LE DONNE, Attilio; Alessandro, Fedeli. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 156:13(2009), pp. 2196-2199. [10.1016/j.topol.2009.04.023]
On metric spaces and local extrema
LE DONNE, Attilio;
2009
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. © 2009 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
