Game strategies yield remote points
type: Item
instance of: scholarly article
title: Game strategies yield remote points
zbMATH Open document ID: 0639.54017
DOI: 10.1016/0166-8641(87)90089-7
author: B. George
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Let X be a nonpseudocompact space. A point \(p\in \beta X-X\) is said to be a remote point of X if for every nowhere dense subset D of X, \(p\not\in Cl_{\beta X}D\). \textit{S. B. Chae} and \textit{J. H. Smith} [Top. Appl. 11, 243-246 (1980; Zbl 0434.54016)] and independently \textit{E. K. van Douwen} [Remote points, Diss. Math. 188 (1981; Zbl 0525.54018)] proved the existence of a large class of spaces having remote points. In this interesting paper the authors prove among other things that a product of metrizable spaces has remote points if and only if it is not compact. Interestingly, their technique of proof uses games.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54D40
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 4042813
zbMATH Keywords: \(\sigma \)-\(\pi \) space
zbMATH Keywords: \(\sigma \)-locally finite \(\pi \)-base
zbMATH Keywords: game strategy
zbMATH Keywords: homogeneity
zbMATH Keywords: nonhomogeneity
zbMATH Keywords: G-space
zbMATH Keywords: N-player game
zbMATH Keywords: recursive strategy
zbMATH Keywords: two-player game
zbMATH Keywords: Stone-Čech compactification
zbMATH Keywords: remote points
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90089-7
OpenAlex ID: W2010450254
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description: scientific article; zbMATH DE number 4042813