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, İtalya, 11 - 13 Eylül 2013, cilt.32, ss.9-16 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 32
  • Doi Numarası: 10.2991/eusflat.2013.2
  • Basıldığı Şehir: Milan
  • Basıldığı Ülke: İtalya
  • Sayfa Sayıları: ss.9-16
  • Anahtar Kelimeler: Fuzzy topology, categorical fuzzy topology, partially ordered set-valued space, augmented partially ordered set, complete partially ordered set, subset system, FOUNDATIONS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.