On kuratowski I–convergence of sequences of closed sets

Creative Commons License

Talo Ö., Sever Y.

Filomat, cilt.31, sa.4, ss.899-912, 2017 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.2298/fil1704899t
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.899-912
  • Anahtar Kelimeler: Hausdorff I–convergence, Ideal convergence, Kuratowski Iȓconvergence, Sequences of sets
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this paper we extend the concepts of statistical inner and outer limits (as introduced by Talo, Sever and Başar) to I–inner and I–outer limits and give some I–analogue of properties of statistical inner and outer limits for sequences of closed sets in metric spaces, where I is an ideal of subsets of the set N of positive integers. We extend the concept of Kuratowski statistical convergence to Kuratowski I–convergence for a sequence of closed sets and get some properties for Kuratowski I–convergent sequences. Also, we examine the relationship between Kuratowski I–convergence and Hausdorff I–convergence.