On a question of Maarten Maurice

Harold Bennett; David Lutzer

doi:10.1016/j.topol.2005.05.004

On a question of Maarten Maurice

Harold Bennett, David Lutzer

Mathematics and Statistics

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6 Scopus citations

Abstract

In this note we give ZFC results that reduce the question of Maarten Maurice about the existence of σ-closed-discrete dense subsets of perfect generalized ordered spaces to the study of very special Baire spaces, and we discuss the current status of the question for spaces with small density. Work of Shelah, Todorčevic, Qiao, and Tall shows that Maurice's problem is undecidable for generalized ordered spaces of local density ω₁.

Original language	English
Pages (from-to)	1631-1638
Number of pages	8
Journal	Topology and its Applications
Volume	153
Issue number	11
DOIs	https://doi.org/10.1016/j.topol.2005.05.004
State	Published - May 1 2006

Keywords

Baire space
Density ω
First-category
GO-space
Heath's question
LOTS
Maurice's question
Nyikos' question
Perfect space
σ-discrete dense set

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10.1016/j.topol.2005.05.004

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AB - In this note we give ZFC results that reduce the question of Maarten Maurice about the existence of σ-closed-discrete dense subsets of perfect generalized ordered spaces to the study of very special Baire spaces, and we discuss the current status of the question for spaces with small density. Work of Shelah, Todorčevic, Qiao, and Tall shows that Maurice's problem is undecidable for generalized ordered spaces of local density ω1.

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KW - Density ω

KW - First-category

KW - GO-space

KW - Heath's question

KW - LOTS

KW - Maurice's question

KW - Nyikos' question

KW - Perfect space

KW - σ-discrete dense set

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JO - Topology and its Applications

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On a question of Maarten Maurice

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Keywords

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