Some topological properties of the spaces of almost null and almost convergent double sequences

Yeşilkayagil M., Başar F.

Turkish Journal of Mathematics, vol.40, no.3, pp.624-630, 2016 (SCI-Expanded, Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2016
  • Doi Number: 10.3906/mat-1504-52
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.624-630
  • Keywords: Almost convergence, Double sequence, Pringsheim convergence
  • Uşak University Affiliated: Yes

Abstract

Let Cf0 and Cf denote the spaces of almost null and almost convergent double sequences, respectively. We show that Cf0 and Cf are BDK-spaces, barreled and bornological, but they are not monotone and so not solid. Additionally, we establish that both of the spaces Cf0 and Cf include the space BS of bounded double series.