Ordinals and scattered compact ordered spaces

Gadi Moran

doi:10.1007/BF01951190

Ordinals and scattered compact ordered spaces

Gadi Moran

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Scattered Compact Ordered Spaces (SCOS) are studied with respect to their well ordered images and preimages. Typical results: (i) A SCOS is homeomorphic to an ordinal iff it has no pit point (a pit in an ordered space is one with infinite left and right cofinalities, one of which is uncountable). (ii) A SCOS of characteristic <μ,m> is mappable onto and includes ω^μ·m+1; it is also an image of ω^μ·(2m)+1. The SCOSs are characterized by: Theorem 5: Let K be a Hausdorff space. The following conditions are equivalent: (a) K is homeomorphic to a compact scattered ordered space. (b) K is an order-two image of a compact ordinal. A.M.S. (MOS) Subject Classification: Primary: 54F05, 54F65, 06A45 Secondary: 54D30.

Original language	English
Pages (from-to)	83-100
Number of pages	18
Journal	Journal of Geometry
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/BF01951190
State	Published - Dec 1981

Keywords

Compact well-ordered space
Order-two image
Order-two mapping
Scattered compact ordered space

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF01951190

Cite this

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Ordinals and scattered compact ordered spaces

Abstract

Keywords

ASJC Scopus subject areas

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