Products of topological spaces and families of filters

被引：0

作者：

Lipparini, Paolo ^{[1
]}

机构：

[1] II Univ Roma Tor Vergata, Dipartimento Matemat, Viale Ricca Ric Sci,Via Cracovia 50, I-00133 Rome, Italy

来源：

COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE | 2023年 / 64卷 / 03期

关键词：

filter convergence; ultrafilter; product; subproduct; sequential compactness; sequencewise P-compactness; Lindel; mu; lambda]of property; final lambda-compactness; lambda]-compactness; Menger property; Rothberger property; COMPACT;

D O I：

10.14712/1213-7243.2024.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelof if and only if all subproducts by <= omega(1) factors are Lindelof. Parallel results are obtained for final omega(n)-compactness, [lambda, mu]-compactness, the Menger and the Rothberger properties.

引用

页码：373 / 394

页数：22

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