关于避免点措施

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-06-07 DOI:10.1016/j.topol.2024.108988

Piotr Borodulin–Nadzieja , Artsiom Ranchynski

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引用次数: 0

摘要

我们说拓扑空间 X 的元素 x 避开度量的条件是：对于 X 上的每一个伯勒度量 μ，如果 μ({x})=0 则存在一个开放的 U∋x，使得 μ(U)=0。这个性质的否定可以看作是支持严格正度量性质的局部版本。我们将研究在一般情况下以及在ω⁎（ω的斯通切赫剩余紧凑化）的背景下避免度量的点。

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On points avoiding measures

We say that an element x of a topological space X avoids measures if for every Borel measure μ on X if $μ ({x}) = 0$ , then there is an open $U ∋ x$ such that $μ (U) = 0$ . The negation of this property can viewed as a local version of the property of supporting a strictly positive measure. We study points avoiding measures in the general setting as well as in the context of $ω^{⁎}$ , the remainder of Stone-Čech compactification of ω.

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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.