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arXiv:1206.6779 [math.GN]AbstractReferencesReviewsResources

On the cardinality of Hausdorff spaces

Filippo Cammaroto, Andrei Catalioto, Jack Porter

Published 2012-06-28, updated 2012-12-17Version 5

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{\i} 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.

Comments: This paper has been withdrawn by the author due to an error in chapter 4
Categories: math.GN
Subjects: 54A25, 54A35
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