递增有界一致连续函数的扩展

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-24 DOI:10.1016/j.topol.2025.109599

Kaori Yamazaki

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引用次数: 0

摘要

本文证明了对于具有预定阶的一致空间X的子空间a上的一个递增有界一致连续函数f，当且仅当f在X上是一致完全序分离的，f可以推广到X上的一个递增有界一致连续函数，从而推广了McShane在度量空间上的可拓定理和kat托夫在一致空间上的定理。此外，我们建立了具有单调一致扩展性质的预定阶的一致/度量空间X的一个表征，回答了e.a.k ok提出的一个问题。

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Extensions of increasing bounded uniformly continuous functions

In this paper, we show that, for an increasing bounded uniformly continuous function f on a subspace A of a uniform space X equipped with a preorder, f can be extended to an increasing uniformly continuous function on X if and only if f is uniformly completely order separated in X. This extends McShane's Extension Theorem for metric spaces and Katětov's Theorem for uniform spaces. Moreover, we establish a characterization of a uniform/metric space X equipped with a preorder possessing the monotone uniform extension property, which answers a question asked by E.A.Ok.

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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.