Search results for "Completely distributive lattice"

showing 3 items of 3 documents

M-bornologies on L-valued Sets

2017

We develop an approach to the concept of bornology in the framework of many-valued mathematical structures. It is based on the introduced concept of an M-bornology on an L-valued set (X, E), or an LM-bornology for short; here L is an iccl-monoid, M is a completely distributive lattice and \(E: X\times X \rightarrow L\) is an L-valued equality on the set X. We develop the basics of the theory of LM-bornological spaces and initiate the study of the category of LM-bornological spaces and appropriately defined bounded “mappings” of such spaces.

Mathematics::Functional AnalysisPure mathematics010102 general mathematicsMathematics::General Topology02 engineering and technology01 natural sciencesSet (abstract data type)Mathematics::K-Theory and HomologyBounded function0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0101 mathematicsMathematical structureCompletely distributive latticeMathematics
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The completely distributive lattice of machine invariant sets of infnite words

2007

Mealy machineDiscrete mathematicsAlgebra and Number TheoryApplied MathematicsDistributive latticeInvariant (mathematics)Completely distributive latticeBirkhoff's representation theoremCongruence lattice problemMathematicsDiscussiones Mathematicae - General Algebra and Applications
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L-fuzzy syntopogenous structures, Part I: Fundamentals and application to L-fuzzy topologies, L-fuzzy proximities and L-fuzzy uniformities

2013

Abstract We introduce the concept of an L-fuzzy syntopogenous structure where L is a complete lattice endowed with an implicator ↦ : L × L → L satisfying certain properties (in particular, as L one can take an MV-algebra). As special cases our L-fuzzy syntopogenous structures contain classical Csaszar syntopogenous structures, Katsaras–Petalas fuzzy syntopogenous structures as well as fuzzy syntopogeneous structures introduced in the previous work of the second named author (A. Sostak, Fuzzy syntopogenous structures, Quaest. Math. 20 (1997) 431–461). Basic properties of the category of L-fuzzy syntopogenous spaces are studied; categories of L-fuzzy topological spaces, L-fuzzy proximity spac…

Discrete mathematicsPure mathematicsComplete latticeMathematics::General MathematicsArtificial IntelligenceLogicStructure (category theory)Topological spaceCompletely distributive latticeNetwork topologyFuzzy logicMathematicsFuzzy Sets and Systems
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