Interior and closure operators on texture spaces-I: Basic concepts and Cech closure operators


DİKER M. , DOST Ş. , UGUR A. A.

FUZZY SETS AND SYSTEMS, cilt.161, ss.935-953, 2010 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 161 Konu: 7
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.fss.2009.09.023
  • Dergi Adı: FUZZY SETS AND SYSTEMS
  • Sayfa Sayısı: ss.935-953

Özet

This paper is the first of a series of three papers oil the theory of interior and closure operators Here. the theory is discussed from the textural point of view. First. the interior and closure operators oil texture spaces are defined and some basic properties are given in terms of neighbourhoods and coneigbourhoods Then the category dfIC whose objects ire interior-closure Spaces and the morphisms are bicontinuous difunctions is shown to he topological over the ground category dfTex of textures and difunctions Further. considering the closure operator oil Hutton algebras (known as fuzzy lattices) in the sense of Cech, the category HutCl of Hutton closure spaces and continuous mappings is defined Finally, the category cdfIC of complemented bicontinuous difunctions and complemented interior-closure texture spaces and the opposite category of HutCl are shown to be equivalent (C) 2009 Elsevier B.V. All rights reserved