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Orthogonal adjointness in posets with
Michal Botur, Ivan Chajda, Helmut Länger
Motivated by the concept of polarity introduced by G. Birkhoff for a binary relation on a set, we introduce a concept of orthogonality in a poset with . A pair of operators ,…
Induced orthogonality in semilattices with 0 and in pseudocomplemented lattices and posets
Ivan Chajda, Miroslav Kolařík, Helmut Länger
On an arbitrary meet-semilattice S with 0 we define an orthogonality relation and investigate the lattice Cl(S) of all subsets of S closed under this orthogonality. We show that if…
Tolerances on posets
Ivan Chajda, Helmut Länger
The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventieth of the twentieth century by B. Zelinka and the first author. Sin…
Conditions forcing the existence of relative complements in lattices and posets
Ivan Chajda, Helmut Länger
It is elementary and well-known that if an element x of a bounded modular lattice L has a complement in L then x has a relative complement in every interval [a,b] containing x. We…