Any perfect GO-space with the underlying LOTS satisfying local perfectness can embed in a perfect LOTS

Shi, Wei-Xue; Miwa, Takuo; Gao, Yin-Zhu

doi:10.1016/s0166-8641(97)88243-0

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Corollary 321

Problem 1 ([1]1

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2006

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Cited by 5 publications

(2 citation statements)

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“…", it might be worthwhile to work in a model of ZFC that contains a Souslin line S, and then try to build a counterexample from S by introducing some isolated points and some one-sided Sorgenfrey points in the usual way. However, that approach cannot work, because in [16] the authors show in ZFC that any GO-space constructed in the usual way on a perfect LOTS will be embeddable in some other perfect LOTS.…”

Section: Corollary 32mentioning

confidence: 99%

On a question of Maarten Maurice

Bennett

Lutzer

2006

Topology and its Applications

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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 ω 1 .

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Section: Corollary 32mentioning

confidence: 99%

On a question of Maarten Maurice

Bennett

Lutzer

2006

Topology and its Applications

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“…In [6] and [7] the author with T. Miwa and Y.-Z. Gao has proved that there exists a perfect GO-space which cannot be densely embedded in any perfect LOTS.…”

Section: Problem 1 ([1]mentioning

confidence: 99%