局部同构的无限林德洛夫 P 群是同构的

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-07-01 DOI:10.1016/j.topol.2024.109005

Mikhail Tkachenko

引用次数: 0

摘要

我们证明了文章标题中的陈述。然后，我们应用它来证明存在林德洛夫群和满足这样的条件，即和不是局部同构的。这从反面解决了本书（Arhangel'skii 和 Tkachenko, 2008 ）中的问题 4.4.7。此外，我们还提出了两个同构的完整阿贝尔群，其中一个是窄群，另一个不是。

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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Locally homeomorphic infinite Lindelof P-groups are homeomorphic

We prove the statement formulated in the title of the article. Then we apply it to show that there exists Lindelöf P-groups G and H satisfying $w (G) = w (H) = | G | = | H | = ℵ_{1}$ such that G and H are not locally homeomorphic. This solves Problem 4.4.7 from the book (Arhangel'skii and Tkachenko, 2008 [1]) in the negative. Also, we present two homeomorphic complete Abelian P-groups one of which is ω-narrow and the other is not.

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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.