Theory of granular lattices and its applications |
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Authors: | Guo-Jun Wang |
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Affiliation: | Institute of Mathematics, Shaanxi Normal University, Xi'an 710062, P.R. China |
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Abstract: | Based on the concept of components of elements of a complete lattice this paper proposed the theory of granular lattices and proved that a topological space X is locally connected if and only if the lattice Ω(X) of its topology is a granular lattice. Moreover, this paper discussed compactness of abstract semantics on certain granular lattices and proved that the semantics is compact if it is continuous in a natural sense, and as a corollary, the compactness of Lukasiewicz's semantics was clarified. |
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Keywords: | Component Granular lattice Locally connected space Abstract semantics Compactness Continuity Lukasiewicz's semantics |
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