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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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
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spelling doaj-3ad1e24903e34023a896ae9b61dbe8852020-11-24T21:40:43ZengSciendoAnnales Mathematicae Silesianae2391-42382019-09-01331415410.2478/amsil-2019-0003amsil-2019-0003Topological Spaces with the Freese–Nation PropertyBąk Judyta0Kucharski Andrzej1Institute of Mathematics, Jan Kochanowski University, Świętokrzyska 15, 25-406 Kielce and Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007 Katowice, PolandInstitute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007Katowice, PolandWe 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.http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0003/amsil-2019-0003.xml?format=INTFNS propertyan inverse limitopenly generated spaceccc54B1054D70
collection DOAJ
language English
format Article
sources DOAJ
author Bąk Judyta
Kucharski Andrzej
spellingShingle Bąk Judyta
Kucharski Andrzej
Topological Spaces with the Freese–Nation Property
Annales Mathematicae Silesianae
FNS property
an inverse limit
openly generated space
ccc
54B10
54D70
author_facet Bąk Judyta
Kucharski Andrzej
author_sort Bąk Judyta
title Topological Spaces with the Freese–Nation Property
title_short Topological Spaces with the Freese–Nation Property
title_full Topological Spaces with the Freese–Nation Property
title_fullStr Topological Spaces with the Freese–Nation Property
title_full_unstemmed Topological Spaces with the Freese–Nation Property
title_sort topological spaces with the freese–nation property
publisher Sciendo
series Annales Mathematicae Silesianae
issn 2391-4238
publishDate 2019-09-01
description 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.
topic FNS property
an inverse limit
openly generated space
ccc
54B10
54D70
url http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0003/amsil-2019-0003.xml?format=INT
work_keys_str_mv AT bakjudyta topologicalspaceswiththefreesenationproperty
AT kucharskiandrzej topologicalspaceswiththefreesenationproperty
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