Products of consonant spaces and Čech complete spaces

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-07-03 DOI:10.1016/j.topol.2025.109495

Francis Jordan

引用次数: 0

Abstract

We characterize those consonant spaces whose product with any Čech complete is again consonant. We then show that in the class of completely regular spaces these spaces generalize spaces that are Menger at infinity. A perfect set theorem is established for these spaces. We also characterize those consonant spaces whose product with any Čech complete space of given hereditary Lindelöf number remains consonant. Various examples are given.

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辅音空间与Čech完全空间的乘积

我们描述那些辅音空间，它们与任何Čech完备的乘积也是辅音。然后我们证明了在完全正则空间中，这些空间推广了无穷远处的门格尔空间。对这些空间建立了一个完全集合定理。我们还描述了那些与给定遗传数Lindelöf的任何Čech完全空间积保持辅音的辅音空间。给出了各种例子。

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.