The largest T2 ⊤-compactification of ⊤-convergence spaces

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2026-02-01 Epub Date: 2025-11-26 DOI:10.1016/j.topol.2025.109673

Yuan Gao, Bin Pang

引用次数: 0

Abstract

The primary objective of this paper is to study the properties of ⊤-closed sets and the largest

T_{2}

⊤-compactification of ⊤-convergence spaces. Firstly, we study some properties of ⊤-ultrafilters and introduce the concept of a ⊤-closed set and the concept of a ⊤-compact set, examining the relationship between them. Secondly, we present the notion of essentially ⊤-compact ⊤-convergence spaces and explore the necessary and sufficient conditions for a ⊤-convergence space to have the largest

T_{2}

⊤-compactification. Finally, we construct the Richardson ⊤-compactification of a ⊤-convergence space and identify the necessary and sufficient conditions for the Richardson ⊤-compactification to be the largest

T_{2}

⊤-compactification within the framework of Kent ⊤-convergence spaces.

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最大的T2，对，收敛空间的紧化

本文的主要目的是研究了收敛空间的最大T2 -紧化的性质。首先，我们研究了超滤子的一些性质，引入了闭集和紧集的概念，并考察了它们之间的关系。其次，我们提出了本质上的，紧的，收敛空间的概念，并探讨了一个，收敛空间具有最大T2，紧化的充分必要条件。最后，构造了一个收敛空间的Richardson -紧化，并确定了在Kent -收敛空间的框架内，Richardson -紧化是最大的T2 -紧化的充分必要条件。

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.