Every finite-dimensional analytic space is σ-homogeneous

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-07-01 DOI:10.1016/j.topol.2024.109004

Claudio Agostini, Andrea Medini

引用次数: 0

Abstract

All spaces are assumed to be separable and metrizable. Building on work of van Engelen, Harrington, Michalewski and Ostrovsky, we obtain the following results:

•
Every finite-dimensional analytic space is σ-homogeneous with analytic witnesses,
•
Every finite-dimensional analytic space is σ-homogeneous with pairwise disjoint $Δ_{2}^{1}$ witnesses.

Furthermore, the complexity of the witnesses is optimal in both of the above results. This answers a question of Medini and Vidnyánszky, and completes the picture regarding σ-homogeneity in the finite-dimensional realm. It is an open problem whether every analytic space is σ-homogeneous. We also investigate finite unions of homogeneous spaces.

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每个有限维解析空间都是σ均质的

假定所有空间都是可分离和可元化的。在 van Engelen、Harrington、Michalewski 和 Ostrovsky 等人的研究基础上，我们得到了以下结果：-每个有限维解析空间都是 σ 均质的，都有解析见证；-每个有限维解析空间都是 σ 均质的，都有成对不相邻的 Δ21 见证。此外，在上述两个结果中，见证的复杂性都是最优的。这回答了梅迪尼和维德尼亚恩斯基提出的一个问题，并完善了有限维领域中的σ同质性。至于是否每个解析空间都是σ均质的，这还是个未决问题。我们还研究了同质空间的有限联合。

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.