Pre-Hausdorff and Hausdorff Proximity Spaces

KULA M., Ozkan S., Marasli T.

FILOMAT, cilt.31, sa.12, ss.3837-3846, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 12
  • Basım Tarihi: 2017
  • Doi Numarası: 10.2298/fil1712837k
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3837-3846
  • Erciyes Üniversitesi Adresli: Evet

Özet

In this paper, an explicit characterization of the separation properties for T-0, T-1, PreT(2) (pre-Hausdorff) and T-2 (Hausdorff) is given in the topological category of proximity spaces. Moreover, specific relationships that arise among the various T-i, i = 0; 1; 2 and PreT(2) structures are examined in this category. Finally, we investigate the relationships among generalized separation properties for Ti, i = 0,1, 2 and PreT(2) (in our sense), separation properties at a point p and separation properties for T-i, i = 0, 1,2 in the usual sense in this category.