HFD spaces in two problems of countably compact like properties

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-03-19 DOI:10.1016/j.topol.2025.109364

Y.F. Ortiz-Castillo , A.H. Tomita

引用次数: 0

Abstract

In this article we will construct a consistent space X such that every power smaller than

2^{c}

of its hyperspace

CL (X)

is countably compact, but its

2^{c}

-power is not countably compact. This provides a consistent negative answer to a question from I. Juhász and J. E. Vaughan [11]. We also give a consistent negative answer to a question from M. Sanchis and A. Tamariz-Mascarúa [13].

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两个可数类紧性问题中的HFD空间

在本文中，我们将构造一个一致空间X，使得它的超空间CL(X)的每个小于2c的幂都是可数紧的，但是它的2c幂不是可数紧的。这为I. Juhász和j.e. Vaughan[11]的问题提供了一致的否定答案。对于M. Sanchis和a . Tamariz-Mascarúa[13]提出的问题，我们也给出了一致的否定答案。

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.