Textures and C-spaces


Demirci M.

FUZZY SETS AND SYSTEMS, vol.158, no.11, pp.1237-1245, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 158 Issue: 11
  • Publication Date: 2007
  • Doi Number: 10.1016/j.fss.2007.01.014
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1237-1245
  • Keywords: texture, C-space, core space, sober space, partially ordered set, completely distributive lattice, FUZZY TOPOLOGY, FOUNDATIONS, PROTEIN
  • Akdeniz University Affiliated: Yes

Abstract

In this paper we point out that textures, simple textures and plain textures are, respectively, isomorphic to C-spaces, sober C-spaces and partially ordered sets. Using the isomorphism between textures and C-spaces, we show that subtextures, quotient textures, sums and products of textures can be identified as subspaces, quotient spaces, sums and products of C-spaces. Furthermore, it is shown that textures, except discrete textures, do not satisfy any separation axioms (T-1,..., T-4) other than To, and so they are not pseudometrizable. Then we also give four useful characterizations of the complete distributivity condition of textures. (C) 2007 Elsevier BN. All rights reserved.