Covering properties by (a)-θ-open sets in (a)topological spaces


Luthra S., Chauhan H. V. S., Tyagi B., Tunç C.

Palestine Journal of Mathematics, vol.11, no.2, pp.531-541, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2022
  • Journal Name: Palestine Journal of Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.531-541
  • Keywords: (a)-θ-compact, (a)-θ-Menger, (a)-θ-open sets, continuous functions, covering properties, Selection principles
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

© Palestine Polytechnic University-PPU 2022.We introduced the concept of (a)-θ-compactness and (a)-θ-Mengerness in (a)topological spaces. We discussed the relationship of the above notions with the other known covering properties. It is shown that the product of two (a)-θ-Menger (resp. (a)-θ-compact) spaces is (a)-θ-Menger (resp. (a)-θ-compact) if one of them is (a)s-compact. If Xi is (a)-θ-Menger for each finite i, then (a)topological space X satisfies the selection principle Sfin(Θ-Ω(X ), Θ-Ω(X)). Further, it is shown that the (a)-θ-Menger covering property is preserved under (a)-θ-continuous and (a)-strongly-θ-continuous map.