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The lattice structure of \(\mathbf{L}\)-contact relations. (English) Zbl 1387.06010

Summary: From the point of view of graded truth approach, we define the notion of a contact relation on the collection of all \(\mathbf{L}\)-sets, discuss the connection to the set of all close, reflexive, and symmetric relations on all \(\mathbf{L}\)-ultrafilters on \(X\), and investigate the algebraic structure of all \(\mathbf{L}\)-contact relations.

MSC:

06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
06B30 Topological lattices
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