Applications of Categorical Fixed-basis Fuzzy Topological Spaces to A-valued Spaces

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DEMİRCİ M.

8th Conference of the European-Society-for-Fuzzy-Logic-and-Technology (EUSFLAT), Milan, Italy, 11 - 13 September 2013, vol.32, pp.9-16, (Full Text)

  • Publication Type: Conference Paper / Full Text
  • Volume: 32
  • Doi Number: 10.2991/eusflat.2013.2
  • City: Milan
  • Country: Italy
  • Page Numbers: pp.9-16
  • Keywords: Fuzzy topology, categorical fuzzy topology, partially ordered set-valued space, augmented partially ordered set, complete partially ordered set, subset system, FOUNDATIONS
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

As an application of the dual equivalence between the category of L-spatial C-objects and the category of L-sober C-M-L-spaces, it is shown in this paper that for a fixed augmented partially ordered set A, there exists a dual equivalence between the category of A-spatial augmented partially ordered sets and the category of A-sober A-valued spaces. Then, with regard to this duality, for a fixed (Z(1), Z(2))complete partially ordered set L, we establish a dual equivalence between the category of L-spatial (Z(1), Z(2))-complete partially ordered sets and the category of L-sober L-valued Q-spaces.