Point-set games and functions with the hereditary small oscillation property

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-06-18 DOI:10.1016/j.topol.2024.109000

Marek Balcerzak , Tomasz Natkaniec , Piotr Szuca

引用次数: 0

Abstract

Given a metric space X, we consider certain families of functions $f : X \to R$ having the hereditary oscillation property HSOP and the hereditary continuous restriction property HCRP on large sets. When X is Polish, among them there are families of Baire measurable functions, $\overline{μ}$ -measurable functions (for a finite nonatomic Borel measure μ on X) and Marczewski measurable functions. We obtain their characterizations using a class of equivalent point-set games. In similar aspects, we study cliquish functions, SZ-functions and countably continuous functions.

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具有遗传小振荡特性的点集博弈和函数

给定一个度量空间 X，我们考虑在大集合上具有遗传振荡性质 HSOP 和遗传连续限制性质 HCRP 的函数 f:X→R 的某些族。当 X 是波兰语时，其中有 Baire 可测函数族、μ‾可测函数族（对于 X 上的有限非原子 Borel 度量 μ）和 Marczewski 可测函数族。我们利用一类等价点集博弈得到了它们的特征。在类似方面，我们还研究了簇函数、SZ 函数和可数连续函数。

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.