离散选择性和不相交局部π基

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-07-31 DOI:10.1016/j.topol.2025.109534

Hector Barriga-Acosta, Alan Dow

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引用次数: 0

摘要

我们肯定地回答了b[3]中Gruenhage和Tkachuk的两个问题。第一个结果是：每一个紧度可数的紧空间在每一点上都有一个可数的不相交的局部π基。第二个结果是，如果一个空间X是遗传的Lindelöf，并且πχ(K，X)>；ω不等式对X的每一个紧集K都成立，那么它是离散选择性的。

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Discrete selectivity and disjoint local π-bases

We answer affirmatively two questions of Gruenhage and Tkachuk from [3]. The first result is that every compact space of countable tightness has a countable disjoint local π-base at every point. The second result is that a space X is discretely selective if it is hereditarily Lindelöf and has the property that the inequality

π χ (K, X) > ω

holds for every compact set K of X.

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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.