弱偏度量空间上的拓扑与不动点

IF 0.5 4区 数学 Q3 MATHEMATICS
Mengqiao Huang , Xiaodong Jia , Qingguo Li
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引用次数: 0

摘要

对于一个弱偏度量空间(X,p),在X上存在一个正则度量mp,定义为mp(X, y)=max (p(X, y) - p(X, X),p(X, y) - p(y,y)},对于所有X, y∈X。我们证明了当且仅当(X,mp)上的度量拓扑与(X,p)上的Lawson拓扑一致时,(X,p)上的偏度量拓扑与(X,p)上的Scott拓扑重合,前提是弱偏度量空间(X,p)是专一阶的定域,且其关联的度量空间(X,mp)是紧的。讨论了弱偏度量空间上自映射的不动点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Topologies and fixpoints on weak partial metric spaces
For a weak partial metric space (X,p), there is a canonical metric mp on X, defined as mp(x,y)=max{p(x,y)p(x,x),p(x,y)p(y,y)} for all x,yX. We prove that the partial metric topology and the Scott topology on (X,p) coincide if and only if the metric topology on (X,mp) and the Lawson topology on (X,p) agree, provided that the weak partial metric space (X,p) is a domain in its specialization order and its associated metric space (X,mp) is compact. We also discussed fixpoints of self maps defined on weak partial metric spaces.
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来源期刊
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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