A note on perfect generalized ordered spaces

Harold R. Bennett; Masami Hosobuchi; David J. Lutzer

doi:10.1216/rmjm/1181070403

A note on perfect generalized ordered spaces

Harold R. Bennett, Masami Hosobuchi, David J. Lutzer

Mathematics and Statistics

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

3 Scopus citations

Abstract

In this paper we examine certain recent generalizations of the topological property "X is perfect," i.e., closed subsets of X are G_δ-sets, to determine which are equivalent to being perfect in the category of generalized ordered spaces. We use these results to give necessary and sufficient conditions for X* and L(X), the two most common linearly ordered extensions of the generalized ordered space A, to be perfect.

Original language	English
Pages (from-to)	1195-1207
Number of pages	13
Journal	Rocky Mountain Journal of Mathematics
Volume	29
Issue number	4
DOIs	https://doi.org/10.1216/rmjm/1181070403
State	Published - 1999

Keywords

Almost perfect
Generalized ordered space
Linearly ordered space
Monotonically normal space
Perfect space
S-normality
Strongly densely normal
Weakly perfect space

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10.1216/rmjm/1181070403

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KW - Generalized ordered space

KW - Linearly ordered space

KW - Monotonically normal space

KW - Perfect space

KW - S-normality

KW - Strongly densely normal

KW - Weakly perfect space

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A note on perfect generalized ordered spaces

Abstract

Keywords

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