On a problem by A. Hajnal and I. Juhász
type: Item
instance of: scholarly article
title: On a problem by A. Hajnal and I. Juhász
zbMATH Open document ID: 1185.54003
author: Nuno C. Freire
author: M. F. Veiga
published in: Vietnam Journal of Mathematics
publication date: 2009-07-14T00:00:00Z
review text: \textit{A. Hajnal} and \textit{I. Juhász} asked in [Problems (p. 637), Topics in topology. Colloquia Mathematica Societatis Janos Bolyai. 8. Amsterdam-London: North-Holland Publishing Company. 643 p. (1974; Zbl 0278.00018)] whether \(\lambda^\omega=\lambda\) whenever \(\lambda\) is the cardinality of a Hausdorff topology on an infinite set. The authors describe an example with the claim that the cardinality of its topology is \(\aleph_\omega (<\aleph_\omega^{\;\omega})\). Unfortunately the topology has cellularity \(\aleph_\omega\) and hence cardinality \(2^{\aleph_\omega}\).
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D10
zbMATH DE Number: 5578070
zbMATH Keywords: number of open sets
zbMATH Keywords: Hausdorff space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5578070