Compact-calibres of regular and monotonically normal spaces
type: Item
instance of: scholarly article
title: Compact-calibres of regular and monotonically normal spaces
zbMATH Open document ID: 0993.54003
DOI: 10.1155/S0161171202011365
author: David W. McIntyre
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49385
full work available at URL: S0161171202011365.html
review text: Summary: A topological space has calibre \(\omega_1\) (resp., calibre \((\omega_1,\omega)\)) if every point-countable (resp., point-finite) collection of nonempty open sets is countable. It has compact-calibre \(\omega_1\) (resp., compact-calibre \((\omega_1,\omega)\)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every disjoint (resp., discrete) collection of nonempty open sets is countable. The relative strengths of these six conditions are determined for Moore spaces, regular first countable spaces, linearly-ordered spaces, and arbitrary regular spaces. It is shown that the relative strengths for spaces with point-countable bases are the same as those for Moore spaces, and the relative strengths for linearly-ordered spaces are the same as those for arbitrary monotonically normal spaces.
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 1780334
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1780334