Definable quotients in locally o-minimal structures

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-06-11 DOI:10.1016/j.topol.2025.109479

Masato Fujita , Tomohiro Kawakami

引用次数: 0

Abstract

Let

F = (F, + . \cdot, <, 0, 1, \dots)

be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied when X is a locally closed definable subset of

F^{n}

and there is a definable proper action of a definable topological group G on X.

查看原文本刊更多论文

局部0极小结构中的可定义商

设F=（F,+⋅,<,0,1，…）是有序域的可定义完备局部0 -极小展开。在满足若干技术条件时，利用可定义等价关系证明了可定义集合的可定义商的存在性。当X是Fn的局部闭可定义子集，且在X上存在一个可定义拓扑群G的可定义固有作用时，满足这些条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.