Universal spaces for some families of rim-scattered spaces
type: Item
instance of: scholarly article
title: Universal spaces for some families of rim-scattered spaces
zbMATH Open document ID: 0766.54023
published in: Tsukuba Journal of Mathematics
publication date: 1993-02-22T00:00:00Z
review text: The families of rim-scattered spaces alluded to in the title are denoted \(R^ k_{text{c}}(\alpha)\) and \(R^ k_{\text{lc}}(\alpha)\) respectively. These spaces are to have a base \(\mathcal B\) of open sets such that the boundary of every element of \(\mathcal B\) has scattered height at most \(\alpha\) and a compactification (in the case of \(R^ k_{\text{lc}}(\alpha)\) a locally compact extension) of scattered height at most \(\alpha+k+1\) (this is deduced from the context; in the paper the parameter \(k\) does not appear in the definitions of \(R^ k_{\text{c}}(\alpha)\) and \(R^ k_{\text{lc}}(\alpha)\)). In this rather technical paper the author constructs universal spaces for the classes \(R^ k_{\text{lc}}(\alpha)\); in fact one can, given a subfamily of \(R^ k_{\text{lc}}(\alpha)\) of size at most \(\mathfrak c\), find a space that contains an almost disjoint (in some sense) family of copies of the elements of the family.
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54G12
Mathematics Subject Classification ID: 54E45
zbMATH DE Number: 109333
zbMATH Keywords: compactification of scattered height
zbMATH Keywords: rim-scattered spaces
author: S. D. Iliadis
reviewed by: K. P. Hart
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496161835
OpenAlex ID: W2106541521
DOI: 10.21099/TKBJM/1496161835
description: scientific article; zbMATH DE number 109333