تقرير
Some properties of Pre-uniform spaces
| العنوان: | Some properties of Pre-uniform spaces |
|---|---|
| المؤلفون: | Lin, Fucai, Xie, Yufan, Wu, Ting, Bao, Meng |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, 54A05, 54C08, 54E05, 54E15 |
| الوصف: | In this paper, we introduce the notions of pre-uniform spaces and pre-proximities and investigate some basic properties about them, where the definition of pre-uniformity here is different with the pre-uniformities which are studied in \cite{BR2016}, \cite{GM2007} and \cite{K2016} respectively. First, we prove that each pre-uniform pre-topology is regular, and give an example to show that there exists a pre-uniform structure on a finite set such that the pre-uniform pre-topology is not discrete. Moreover, we give three methods of generating (strongly) pre-uniformities, that is, the definition of a pre-base, a family of strongly pre-uniform covers, or a family of strongly pre-uniform pseudometrics. As an application, we show that each strongly pre-topological group is completely regular. Finally, we pose the concept of the pre-proximity on a set and discuss some properties of the pre-proximity. Comment: 17 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.10725 |
| رقم الأكسشن: | edsarx.2203.10725 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |