Topological spaces with the Freese-Nation property Ⅱ

摘要

The aim of this paper is to study the class of spaces with the FNS property and the it-FNS property. We prove that compact Hausdorff spaces with the FNS property for some base consisting of co-zero sets are openly generated spaces and spaces with the it-FNS property are skeletally generated spaces. We give examples of families without the Freese-Nation property. (c) 2021 Elsevier B.V. All rights reserved.