重温 MSNR 空间

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-11-08 DOI:10.1016/j.topol.2024.109132

John E. Porter

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引用次数: 0

摘要

我们重温了 Stares 于 1996 年提出的单调半邻域精炼（MSNR）空间。MSNR 空间被证明是有序 (F) 的裂片空间。我们还探讨了 MSNR 空间与其他单调覆盖性质之间的关系。我们证明了不具有单调局部有限精炼算子的 MSNR 空间的存在，以及具有单调局部有限精炼算子但不是 MSNR 的空间的存在，回答了 Popvassilev 和 Porter 提出的一个问题。一般来说，紧凑的 MSNR 空间可能不是可元化的，但紧凑的 MSNR LOTS 却是可元化的。其底层 LOTS 具有 σ 闭离散密集子集的 GO 空间被证明具有单调星限精炼算子。

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MSNR spaces revisited

We revisit monotonically semi-neighborhood refining (MSNR) spaces which were introduced by Stares in 1996. MSNR spaces are shown to be lob-spaces with well-ordered (F). The relationships between MSNR spaces with other monotone covering properties are also explored. We show the existence of MSNR spaces that do not posses a monotone locally-finite refining operator and spaces with a monotone locally-finite refining operator that are not MSNR answering a question of Popvassilev and Porter. Compact MSNR spaces may not be metrizable in general, but compact MSNR LOTS are. GO-spaces whose underlying LOTS has a σ-closed-discrete dense subset are shown to have a monotone star-finite refining operator.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.