A generalization of the equality p(X) = a(C-p(X))


Vural Ç.

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, vol.12, no.1, pp.81-84, 2006 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2006
  • Journal Name: BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.81-84
  • Gazi University Affiliated: Yes

Abstract

Suppose that alpha is a family of subsets of a Tychonoff space X and m is an infinite cardinal. We define two new cardinal invariants p(m)(alpha)(X) and a(m)(X) which are generalizations of the point-finite cellularity p(X) of the space X and the Alexandroff number a(X) of the space X, respectively. Then we obtain the equality m center dot p(m)(alpha)(X) = m center dot a(m)(C-alpha(X)). This result implies that p(alpha)(X) = a(C-alpha(X)) and generalizes the equality p(X) = a(C-P(X)) established by Tkachuk in [1].