Topological Spaces with the Freese–Nation Property

Author:

Bąk Judyta1,Kucharski Andrzej2

Affiliation:

1. Institute of Mathematics , Jan Kochanowski University , Świętokrzyska 15, 25-406 Kielce and Institute of Mathematics , University of Silesia in Katowice , Bankowa 14, 40-007 Katowice , Poland

2. Institute of Mathematics , University of Silesia in Katowice , Bankowa 14, 40-007 Katowice , Poland

Abstract

Abstract We give a proposal of generalization of the Freese–Nation property for topological spaces. We introduce a few properties related to Freese–Nation property: FNS, FN, FNS*, FNI. This article presents some relationship between these concepts. We show that spaces with the FNS property satisfy ccc and any product of such spaces also satisfies ccc. We show that all metrizable spaces have the FN property.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Topological spaces with the Freese–Nation property II;Topology and its Applications;2021-12

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