Intersection properties of open sets
type: Item
instance of: scholarly article
title: Intersection properties of open sets
zbMATH Open document ID: 0582.54003
DOI: 10.1016/0166-8641(85)90001-X
author: István Juhász
author: Andras Hajnal
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: Call a \(T_ 2\)-space \(P_ 1\) \((P_ 2)\) if whenever U and V are disjoint and open both (one of) U and V must be countable. The authors investigate the possible sizes of such spaces. They obtain the following results: (i) every \(P_ 2\)-space is of size at most \(2^{\omega}\), (ii) there is a \(P_ 1\)-space of size \(2^{\omega}\), (iii) there is a regular \(P_ 2\)-space of size \(2^{\omega}\), (iv) there is a compact \(P_ 2\)-space of size \(\omega_ 1\) and (v) if \(2^{\omega}\) is big then compact \(P_ 2\)-spaces of size \(2^{\omega}\) may or may not exist.
reviewed by: K. P. Hart
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54A35
zbMATH DE Number: 3931969
zbMATH Keywords: 0-dimensional space
zbMATH Keywords: Hausdorff space
zbMATH Keywords: cardinality of open sets
zbMATH Keywords: size of open sets
MaRDI profile type: Publication
cites work: Set theory. An introduction to independence proofs
full work available at URL: 0166-8641(85)90001-x
OpenAlex ID: W2088181977
Wikidata QID: Q128099415
description: scientific article; zbMATH DE number 3931969