The Δ1-property of X is equivalent to the Choquet property of B1(X)

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-04-23 DOI:10.1016/j.topol.2025.109395

Alexander V. Osipov

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引用次数: 0

Abstract

We give a characterization of the

Δ_{1}

-property of any Tychonoff space X in terms of the function space

B_{1} (X)

of all Baire-one real-valued functions on a space X with the topology of pointwise convergence. We establish that for a Tychonoff space X the

Δ_{1}

-property is equivalent to the Choquet property of

B_{1} (X)

. Also we construct under ZFC an example of a separable pseudocompact space X such that

C_{p} (X)

is κ-Fréchet-Urysohn but X fails to be a

Δ_{1}

-space. This answers a question of Ka̧kol-Leiderman-Tkachuk.

查看原文本刊更多论文

X的Δ1-property等价于B1(X)的Choquet性质

在具有点向收敛拓扑的空间X上的所有bair - 1实值函数的函数空间B1(X)中，给出了任意Tychonoff空间X的Δ1-property的刻画。我们建立了对于Tychonoff空间X， Δ1-property等价于B1(X)的Choquet性质。在ZFC下构造了一个可分离伪紧空间X的例子，使得Cp(X)为κ- fr - urysohn，但X不为Δ1-space。这就回答了卡科尔-莱德曼-特卡丘克的一个问题。

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.