GDL

Journal from gdlhub / 2017-08-21 11:16:38
Oleh : Sergey A. Solovyov, Fuzzy Information and Engineering
Dibuat : 2014-12-21, dengan 1 file

Keyword : Adjoint situationCategorical equivalenceDualitySchizophrenic objectSober spaceSpatial algebraVariety-based topology
Url : http://www.sciencedirect.com/science/article/pii/S1616865815000023
Sumber pengambilan dokumen : web

The manuscript continues our study on developing a categorically-algebraic (catalg) analogue of the theory of natural dualities of D. Clark and B. Davey, which provides a machinery for obtaining topological representations of algebraic structures. The new setting differs from its predecessor in relying on catalg topology, introduced lately by the author as a new approach to topological structures, which incorporates the majority of both crisp and many-valued developments, ultimately erasing the border between them. Motivated by the variable-basis lattice-valued extension of the Stone representation theorems done by S. E. Rodabaugh, we have recently presented a catalg version of the Priestley duality for distributive lattices, which gave rise (as in the classical case) to a fixed-basis variety-based approach to natural dualities. In this paper, we extend the theory to variable-basis, whose setting is completely different from the respective one of S. E. Rodabaugh, restricted to isomorphisms between the underlying lattices of the spaces.

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