Topological spaces with the Freese–Nation property



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.


Keywords

FNS property; an inverse limit; openly generated space; ccc

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Published : 2019-05-09


BąkJ., & KucharskiA. (2019). Topological spaces with the Freese–Nation property. Annales Mathematicae Silesianae, 33, 41-54. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13649

Judyta Bąk 
Instytut Matematyki, Uniwersytet Jana Kochanowskiego w Kielcach oraz Instytut Matematyki, Uniwersytet Śląski w Katowicach  Poland
Andrzej Kucharski  andrzej.kucharski@us.edu.pl
Instytut Matematyki, Uniwersytet Śląski w Katowicach  Poland



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