Mappings between bornological spaces

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-03-18 DOI:10.1016/j.topol.2025.109344

Gerald Beer , Homeira Pajoohesh

引用次数: 0

Abstract

Let

(X, B)

be a bornological space, i.e., a set X equipped with a bornology

B

of its subsets. Two bornological spaces are considered isomorphic if there is a bijection h between them such that h and its inverse are both bornological maps. We characterize up to isomorphism the bornological images, the coercive images, and the bornological, coercive images of

(X, B)

. In the process we introduce the notion of bornological decomposition space of a bornological space, an analog of the notion of topological decomposition space. Separately, we end the paper by representing a bornological space

(X, B)

as a join semilattice homomorphism from the power set of X to

{0, 1}

that maps each singleton subset to zero.

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性学空间之间的映射

设 (X,B) 是一个生理学空间，即一个集合 X 及其子集的生理学 B。如果两个生理学空间之间存在双射 h，且 h 及其逆映射都是生理学映射，那么这两个生理学空间被认为是同构的。我们将描述 (X,B) 的生理学映像、强制映像和生理学强制映像的同构性。在此过程中，我们引入了生理学空间的生理学分解空间概念，即拓扑分解空间的类似概念。在本文的最后，我们将生理学空间（X,B）表示为从 X 的幂集到 {0,1} 的连接半格同态，它将每个单子集映射为零。

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.