<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Topological Spaces with the Freese–Nation Property

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Topological Spaces with the Freese\u2013Nation 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:...

Topological Spaces with the Freese–Nation Property

Published Online: Jul 18, 2019

Page range: 41 - 54

Received: Nov 30, 2018

Accepted: Apr 09, 2019

DOI: https://doi.org/10.2478/amsil-2019-0003

Keywords
FNS property, an inverse limit, openly generated space, ccc

© 2019 Judyta Bąk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Topological Spaces with the Freese–Nation Property

Published Online: Jul 18, 2019

Page range: 41 - 54

Received: Nov 30, 2018

Accepted: Apr 09, 2019

DOI: https://doi.org/10.2478/amsil-2019-0003

KeywordsFNS property, an inverse limit, openly generated space, ccc

© 2019 Judyta Bąk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
FNS property, an inverse limit, openly generated space, ccc