Category-theoretic fuzzy topological spaces and their dualities

Demirci M.

FUZZY SETS AND SYSTEMS, vol.227, pp.1-24, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 227
  • Publication Date: 2013
  • Doi Number: 10.1016/j.fss.2013.02.013
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-24
  • Keywords: Category theory, Categorical topology, Adjoint situation, Duality, Lattice-valued topology, Many-valued topology, Fuzzy topology, SEPARATION AXIOMS, FOUNDATIONS, REPRESENTATIONS, COMPACTNESS
  • Akdeniz University Affiliated: Yes

Abstract

It is shown in this paper that various approaches to fuzzy topological spaces can be extended to an abstract category C. In this respect, variety-based generalized topological spaces, variable-basis fuzzy topological spaces, fixed-basis fuzzy topological spaces and Hutton fuzzy topological spaces are defined in C. We also construct their respective categories, as well as establish a generalized Papert-Papert-Isbell style adjunction for each of them. These adjunctions are later on refined to equivalences, involving appropriate definitions of spatiality and sobriety. (C) 2013 Elsevier B.V. All rights reserved.