Generic classes defined by neighborhoods assignments and stars

IF 0.5 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2025-01-01 Epub Date: 2024-11-26 DOI:10.1016/j.topol.2024.109147

Iván Martínez-Ruiz , Alejandro Ramírez-Páramo

引用次数: 0

Abstract

In this article we have a couple of mains. The first one is to make a generic exposure on the classes that are obtained by using neighborhood assignments or applying the star operator to a given topological property

P

. The second one is to perform an analysis on the classes defined in the first part of the work, for the numerability property.

It is important to note that in Example 3.13 we present a Hausdorff weakly star countable space which is not feebly Lindelof, which gives a negative response to the Question 3.14 from [1].

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由邻域赋值和星型定义的泛型类

在本文中，我们有几个主要内容。第一个是对通过使用邻域分配或对给定拓扑性质p应用星型运算符获得的类进行一般公开；第二个是对工作的第一部分中定义的类进行可数性分析。值得注意的是，在例3.13中，我们给出了一个Hausdorff弱星可数空间，它不是弱林德洛夫空间，它对来自[1]的问题3.14给出了一个否定的响应。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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