Abstract

This article is a continuation of the study of bornological open covers and related selection principles in metric spaces done in (Chandra et al. 2020 [6]) using the idea of strong uniform convergence (Beer and Levi, 2009 [3]) on a bornology. Here we explore further ramifications, presenting characterizations of various selection principles related to certain classes of bornological covers using the Ramseyan partition relations, interactive results between the cardinalities of bornological bases and certain selection principles involving bornological covers which have not been studied before. Further, some new observations on the -Hurewicz property introduced in [6] and several results on the -Gerlits-Nagy property (which is introduced here following the seminal work of [9]) are presented.

摘要

本文是对强空间统一收敛（Beer和Levi，2009 [3]）的研究（Chandra等人，2020 [6]）在公制空间中进行的出生学开放覆盖和相关选择原理研究的延续。胎教。在这里，我们探索进一步的结果，使用拉姆西扬分区关系，介绍与某些类别的胎教科目有关的各种选择原则的特征，出生学基础的基数之间的互动结果以及涉及胎教科目的某些先前未曾研究过的选择原则。此外，还介绍了[6]中引入的有关-Hurewicz属性的一些新观察结果和-Gerlits-Nagy属性的一些结果（在[9]的开创性工作之后引入）。