Egorov ideals

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-10-21 DOI:10.1016/j.topol.2024.109112

引用次数: 0

Abstract

We study Egorov ideals, that is ideals on ω for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological

Σ_{2}^{0}

ideal is Egorov if and only if it is countably generated. In particular, up to isomorphism, there are only three non-pathological

Σ_{2}^{0}

Egorov ideals. On the other hand, we construct

2^{ω}

pairwise non-isomorphic Borel Egorov ideals. Moreover, we characterize when a product of ideals is Egorov.

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叶戈罗夫的理想

我们研究埃戈罗夫理想，即关于点收敛和均匀收敛的理想版本的埃戈罗夫定理成立的 ω 上的理想。我们证明，当且仅当一个非病理性 Σ20 理想是可数生成的，它才是埃戈罗夫理想。特别是，在同构情况下，只有三个非病理性 Σ20 Egorov 理想。另一方面，我们构造了 2ω 个成对非同构的 Borel Egorov 理想。此外，我们还描述了什么情况下理想的乘积是 Egorov 理想。

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.