Cleavability over ordinals

In this paper we show that if X is an infinite compactum cleavable over an ordinal, then X must be homeomorphic to an ordinal. X must also therefore be a LOTS. This answers two fundamental questions in the area of cleavability. We also leave it as an open question whether cleavability of an infinite...

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Bibliographic Details
Published in:arXiv.org 2012-03
Main Author: Levine, Shari S
Format: Article
Language:English
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Summary:In this paper we show that if X is an infinite compactum cleavable over an ordinal, then X must be homeomorphic to an ordinal. X must also therefore be a LOTS. This answers two fundamental questions in the area of cleavability. We also leave it as an open question whether cleavability of an infinite compactum X over an ordinal \lambda implies X is embeddable into \lambda.
ISSN:2331-8422