Dispersion points and continuous functions
type: Item
instance of: scholarly article
title: Dispersion points and continuous functions
zbMATH Open document ID: 0642.54032
DOI: 10.1016/0166-8641(88)90044-2
author: Hidefumi Katsuura
published in: Topology and its Applications
publication date: 1988-01-01T00:00:00Z
review text: The following question was raised by Gobb and Voxman in 1980: If X is a connected space with a dispersion point p, and f is a nonconstant continuous function on X into X, is \(f(p)=p?\) This paper shows, via a counterexample, that the answer is no. Three related theorems dealing with dispersion points are also exhibited.
Mathematics Subject Classification ID: 54F50
Mathematics Subject Classification ID: 54B15
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 4046666
zbMATH Keywords: fixed points
zbMATH Keywords: quasi-components
zbMATH Keywords: dispersion points
MaRDI profile type: Publication
full work available at URL: 0166-8641(88)90044-2
OpenAlex ID: W2026763918
cites work: Dispersion Points and Fixed Points
cites work: Countable connected spaces
cites work: A Countable Connected Urysohn Space Containing a Dispersion Point
cites work: A countable Hausdorff space with a dispersion point
cites work: Countable Connected Spaces
cites work: A countable connected Urysohn space with a dispersion point
cites work: A countable connected Urysohn space with a dispersion point that is regular almost everywhere
description: scientific article; zbMATH DE number 4046666