Ordinals and scattered compact ordered spaces
type: Item
instance of: scholarly article
title: Ordinals and scattered compact ordered spaces
zbMATH Open document ID: 0545.54022
DOI: 10.1007/BF01951190
author: Gadi Moran
published in: Journal of Geometry
publication date: 1981-01-01T00:00:00Z
review text: The author studies scattered compact linearly ordered spaces (SCOS). A scattered space is one which has no dense-in-itself subset. He relates these spaces to compact well-ordered spaces and to spaces of ordinals. His first theorem states that a SCOS is homeomorphic to a compact well- ordered space only if it has no pit-points. A pit-point has infinite left and right cofinalities, one of which is uncountable. The characteristic ch(K) of a space K is \(<\mu,m>\) if \(\mu\) is the first ordinal such that the derived set \(K^{(\mu +1)}\) is empty, while \(K^{(\mu)}\) has m elements. If ch(K) of a SCOS space K is \(<\mu,m>\), the author shows that there is a continuous mapping of K onto \(\omega^{\mu}\cdot m+1\). If s is the number of symmetric pit-points of K, there is a continuous mapping of \(\omega^{\mu}\cdot(m+s)+1\) onto K, and K contains a closed subspace W homeomorphic to \(\omega^{\mu}\cdot m+1\). He states without proof that K is a SCOS only if K is an order-two continuous image of a compact well- ordered space.
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 3868204
zbMATH Keywords: scattered compact linearly ordered spaces
zbMATH Keywords: compact well-ordered spaces
zbMATH Keywords: spaces of ordinals
zbMATH Keywords: order-two continuous image
reviewed by: O. jun. Frink
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3868204