Topological Spaces with the Freese–Nation Property

Topological Spaces with the Freese–Nation Property

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 an...

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Bibliographic Details
Main Authors: Bąk Judyta, Kucharski Andrzej
Format: Article
Language:English
Published: Sciendo 2019-09-01
Series:Annales Mathematicae Silesianae
Subjects:
FNS property
an inverse limit
openly generated space
ccc
54B10
54D70
Online Access:http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0003/amsil-2019-0003.xml?format=INT
Description
Summary: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.
ISSN:2391-4238

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