Pre-Hausdorff and Hausdorff Proximity Spaces


KULA M. , Ozkan S. , Marasli T.

FILOMAT, vol.31, no.12, pp.3837-3846, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 12
  • Publication Date: 2017
  • Doi Number: 10.2298/fil1712837k
  • Title of Journal : FILOMAT
  • Page Numbers: pp.3837-3846

Abstract

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.