Order embedding theorems and multi-utility representation of the preorder

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-07-03 DOI:10.1016/j.topol.2024.109007

Kaori Yamazaki

引用次数: 0

Abstract

As an improvement of Fletcher-Lindgren order embedding theorem, we show that every completely regular ordered space X is order embedded in the Tychonoff ordered cube of infinite weight of X. For that purpose, we evaluate the minimal cardinality of continuous functions which represent multi-utility of the (pre)order on X. Moreover, for a topological preordered space X which admits a continuous multi-utility representation (or a completely regular ordered space X) and its compact subspace, similar descriptions by maps to Tychonoff ordered cube are also given.

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序嵌入定理和前序的多效用表示

作为对弗莱彻-林格伦有序嵌入定理的改进，我们证明了每个完全正则有序空间 X 都有序嵌入到 X 的无穷重的泰克诺夫有序立方体中。

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.

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