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On the cardinality of Hausdorff spaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2013Embargo end date: 01 Jan 2012 Italy Publisher:Elsevier BVJournal:Topology and its Applications, volume 160, pages 137-142 (issn: 0166-8641,

Authors: CAMMAROTO, Filippo; CATALIOTO, ANDREI; J. Porter;

doi: 10.1016/j.topol.2012.10.007 , 10.48550/arxiv.1206.6779

arXiv: http://arxiv.org/abs/1206.6779

handle: 11570/2435833

On the cardinality of Hausdorff spaces

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Abstract

A common generalization for two of the main streams of cardinality inequalities is developed; each stream derives from the famous inequality established by A.V. Arhangel'ski\u�� in 1969 for Hausdorff spaces. At the end of one stream is the recent inequality by Bella and at the end of the second stream is the 1988 inequality by Bella and Cammaroto. This generalization is extended and used to analyze a result containing an increasing chain of spaces that satisfies the same cardinality inequality. The paper is concluded with some open problems.

This paper has been withdrawn by the author due to an error in chapter 4

Country

Italy

Related Organizations

University of Messina
Italy
University of Kansas
United States

Keywords

54A25, 54A35, General Topology (math.GN), FOS: Mathematics, Geometry and Topology, Hausdorff spaces; cardinal functions; cardinal inequalities; closed pseudo-character; kappa-almost Lindelöf degree; almost Lindelöf pseudo-character; free sequences number; increasing chain of spaces; Hausdorff number., Mathematics - General Topology

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