Star covering properties and neighborhood assignments

Authors

  • Fortunata Aurora Basile
  • Maddalena Bonanzinga Università degli Studi di Messina
  • Fortunato Maesano Università degli Studi di Messina
  • Dmitri B. Shakhmatov Ehime University

DOI:

https://doi.org/10.1478/AAPP.1011A7

Keywords:

star covering properties, Menger, Lindelof, compact

Abstract

Following the idea of van Mill, Tkachuk, and Wilson (2007), we define a space X to be neighborhood assignment P (briefly NA-P, where P is a class of topological spaces) if for any neighbourhood assignment {Ox : x ∈ X} there is a subspace Y ⊂ X such that Y has the property P and ⋃x∈Y Ox = X. In this paper we investigate the classes of NA-P spaces and compare them with the star covering properties for some class of topological spaces P.

Author Biographies

  • Maddalena Bonanzinga, Università degli Studi di Messina
    Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra
  • Fortunato Maesano, Università degli Studi di Messina
    Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra
  • Dmitri B. Shakhmatov, Ehime University
    Division of Mathematics, Physics and Earth Sciences, Graduate School of Science and Engineering, Matsuyama 790-8577, Japan

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Published

2023-03-22

Issue

Vol. 101 No. 1 (2023)

Section

Articles

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