Transfer of information about \(\beta\) N - N via open remainder maps
type: Item
instance of: scholarly article
title: Transfer of information about \(\beta\) N - N via open remainder maps
zbMATH Open document ID: 0709.54020
author: Eric K. van Douwen
published in: Illinois Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The purpose of the paper is to give new tools, in which the information is passed indirectly from \(\beta\) N-N to the Čech-Stone remainder of other spaces. Among them there is the following Open Mapping Lemma: if X is realcompact and non-compact and \(x\in \beta X-X\), then there exists a compact subset of \(\beta\) X-X which contains x and admits an open mapping onto \(\beta\) N-N. Using these theorems, as well as some similar but much more complicated, the author obtained significant new results concerning P-points, \({\mathfrak c}\)-points, \(G_{\delta}\)-subsets, Baire number, character and Hausdorff gaps in the Čech-Stone remainders of locally compact realcompact spaces. The same problems are also investigated in the classes of \(\sigma\)-compact and non-pseudocompact spaces.
Mathematics Subject Classification ID: 54D40
Mathematics Subject Classification ID: 54D60
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54A35
zbMATH DE Number: 4166041
zbMATH Keywords: open retration
zbMATH Keywords: minimum character
zbMATH Keywords: spaces of uniform ultrafilters
zbMATH Keywords: ZFC
zbMATH Keywords: Stone extension
zbMATH Keywords: Cech-Stone remainder of the countable discrete space
zbMATH Keywords: Open Mapping Lemma
zbMATH Keywords: P-points
zbMATH Keywords: \({\mathfrak c}\)-points
zbMATH Keywords: \(G_{\delta }\)- subsets
zbMATH Keywords: Baire number
zbMATH Keywords: Hausdorff gaps
zbMATH Keywords: Čech-Stone remainders of locally compact realcompact spaces
zbMATH Keywords: \(\sigma \) -compact and non- pseudocompact spaces
reviewed by: Aleksander Błaszczyk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4166041