On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces

ÖNAL S., VURAL Ç.

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, vol.11, no.9, pp.1635-1642, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 9
  • Publication Date: 2013
  • Doi Number: 10.2478/s11533-013-0271-3
  • Journal Name: CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1635-1642
  • Middle East Technical University Affiliated: Yes

Abstract

We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x a X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of omega-rank, then X is metaLindelof as well as a countable product of them. We also prove that if W satisfies omega-rank (F) and, for every x a X, W(x) is of the form W (0)(x) a(a) W (1)(x), where W (0)(x) is Noetherian and W (1)(x) consists of neighbourhoods of x, then X is metacompact.