The monotone Lindelöf property and separability in ordered spaces

H. Bennett; D. Lutzer; M. Matveev

doi:10.1016/j.topol.2004.05.015

The monotone Lindelöf property and separability in ordered spaces

H. Bennett, D. Lutzer, M. Matveev

Mathematics and Statistics

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

27 Scopus citations

Abstract

In this paper we investigate the relation between separability and the monotone Lindelöf property in generalized ordered (GO)-spaces. We examine which classical examples are or are not monotonically Lindelöf. Using a new technique for investigating open covers of GO-spaces, we show that any separable GO-space is hereditarily monotonically Lindelöf. Finally, we investigate the relation between the hereditarily monotonically Lindelöf property and the Souslin problem.

Original language	English
Pages (from-to)	180-186
Number of pages	7
Journal	Topology and its Applications
Volume	151
Issue number	1-3 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.topol.2004.05.015
State	Published - Jun 1 2005

Keywords

GO-space
Generalized ordered space
Monotone Lindelöf property
Separability

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10.1016/j.topol.2004.05.015

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AB - In this paper we investigate the relation between separability and the monotone Lindelöf property in generalized ordered (GO)-spaces. We examine which classical examples are or are not monotonically Lindelöf. Using a new technique for investigating open covers of GO-spaces, we show that any separable GO-space is hereditarily monotonically Lindelöf. Finally, we investigate the relation between the hereditarily monotonically Lindelöf property and the Souslin problem.

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KW - Separability

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The monotone Lindelöf property and separability in ordered spaces

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