The answers to two problems on maximal point spaces of domains

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2025-03-12 DOI:10.1016/j.topol.2025.109340

Xiaoyong Xi , Chong Shen , Dongsheng Zhao

引用次数: 0

Abstract

A topological space is domain-representable (or, has a domain model) if it is homeomorphic to the maximal point space

Max (P)

of a domain P (with the relative Scott topology). We first construct an example to show that the set of maximal points of an ideal domain P need not be a

G_{δ}

-set in the Scott space ΣP, thereby answering an open problem from Martin (2003). In addition, Bennett and Lutzer (2009) asked whether X and Y are domain-representable if their product space

X \times Y

is domain-representable. This problem was first solved by Önal and Vural (2015). In this paper, we provide a new approach to Bennett and Lutzer's problem.

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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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