Countable successor ordinals as generalized ordered topological spaces

Robert Bonnet; Arkady Leiderman

doi:10.1016/j.topol.2018.03.032

Countable successor ordinals as generalized ordered topological spaces

Robert Bonnet, Arkady Leiderman

Department of Mathematics

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

1 Scopus citations

Abstract

We prove the following Main Theorem: Every continuous image of a Hausdorff topological space X is a generalized ordered space if and only if X is homeomorphic to a countable successor ordinal (with the order topology). This is a generalization of E. van Douwen's result about orderable spaces.

Original language	English
Pages (from-to)	197-202
Number of pages	6
Journal	Topology and its Applications
Volume	241
DOIs	https://doi.org/10.1016/j.topol.2018.03.032
State	Published - 1 Jun 2018

Keywords

Compact spaces
Continuous images
Generalized ordered topological spaces
Linearly ordered topological spaces

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2018.03.032

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title = "Countable successor ordinals as generalized ordered topological spaces",

abstract = "We prove the following Main Theorem: Every continuous image of a Hausdorff topological space X is a generalized ordered space if and only if X is homeomorphic to a countable successor ordinal (with the order topology). This is a generalization of E. van Douwen's result about orderable spaces.",

keywords = "Compact spaces, Continuous images, Generalized ordered topological spaces, Linearly ordered topological spaces",

author = "Robert Bonnet and Arkady Leiderman",

note = "Funding Information: The first listed author gratefully acknowledges the financial support he received from the Center for Advanced Studies in Mathematics of the Ben-Gurion University of the Negev. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

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doi = "10.1016/j.topol.2018.03.032",

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AU - Leiderman, Arkady

N1 - Funding Information: The first listed author gratefully acknowledges the financial support he received from the Center for Advanced Studies in Mathematics of the Ben-Gurion University of the Negev. Publisher Copyright: © 2018 Elsevier B.V.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We prove the following Main Theorem: Every continuous image of a Hausdorff topological space X is a generalized ordered space if and only if X is homeomorphic to a countable successor ordinal (with the order topology). This is a generalization of E. van Douwen's result about orderable spaces.

AB - We prove the following Main Theorem: Every continuous image of a Hausdorff topological space X is a generalized ordered space if and only if X is homeomorphic to a countable successor ordinal (with the order topology). This is a generalization of E. van Douwen's result about orderable spaces.

KW - Compact spaces

KW - Continuous images

KW - Generalized ordered topological spaces

KW - Linearly ordered topological spaces

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M3 - Article

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VL - 241

SP - 197

EP - 202

JO - Topology and its Applications

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ER -

Countable successor ordinals as generalized ordered topological spaces

Abstract

Keywords

ASJC Scopus subject areas

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