Countably tight, zero-dimensional and totally disconnected dense subspaces of Cp(X)

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-01-21 DOI:10.1016/j.topol.2025.109220

Joel Aguilar-Velázquez , Reynaldo Rojas-Hernández

引用次数: 0

Abstract

In this paper we prove that under CH there exists a space X such that

C_{p} (X)

does not admit dense subspaces of countable tightness, partially answering Problem 1 of [13]. We prove that if X has cardinality at most continuum, then

C_{p} (X)

contains a dense zero-dimensional subspace and a dense totally disconnected non zero-dimensional subspace. We also provide an example of a compact space X such that

C_{p} (X, 2)

is exponentially separable but X is not Corson compact.

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Cp(X)的可数紧、零维、完全不连通的稠密子空间

本文证明了CH下存在一个空间X，使得Cp(X)不存在紧度可数的密子空间，部分回答了[13]的问题1。证明了如果X在最大连续域中具有基数，则Cp(X)包含一个稠密的零维子空间和一个稠密的完全不连通的非零维子空间。我们还提供了一个紧空间X的例子，使得Cp（X,2）是指数可分的，但X不是Corson紧的。

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.