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

Vural Ç.

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, cilt.12, sa.1, ss.81-84, 2006 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 1
  • Basım Tarihi: 2006
  • Dergi Adı: BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.81-84
  • Gazi Üniversitesi Adresli: Evet

Özet

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].