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A characterization of polarities whose polar lattice is orthomodular

Roman R. Zapatrin (1996)

Czechoslovak Mathematical Journal

A constructive characterization of the lattices of all retractions, preclosure, quasi-closure and closure operators on a complete lattice

Cousot, Patrick, Cousot, Radhia (1979)

Portugaliae mathematica

A counterexample to a result concerning closure operators.

Ranzato, F. (2001)

Portugaliae Mathematica. Nova Série

A Galois connection between distance functions and inequality relations

Árpád Száz (2002)

Mathematica Bohemica

Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set $S$ and inequality relations on $X_{S} = S \times ℝ$ . Moreover, we also investigate a relationship between the functions of $S$ and $X_{S}$ .

A Galois correspondence for boolean algebras

L. Varecza (1975)

Matematički Vesnik

A Galois correspondence for universal algebras

L. Varecza (1979)

Matematički Vesnik

A selection theorem for Boolean correspondences.

Siegfried Graf (1977)

Journal für die reine und angewandte Mathematik

Adjoint Semilattice and Minimal Brouwerian Extensions of a Hilbert Algebra

Jānis Cīrulis (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let $A : = (A, \to, 1)$ be a Hilbert algebra. The monoid of all unary operations on $A$ generated by operations $α_{p} : x \mapsto (p \to x)$ , which is actually an upper semilattice w.r.t. the pointwise ordering, is called the adjoint semilattice of $A$ . This semilattice is isomorphic to the semilattice of finitely generated filters of $A$ , it is subtractive (i.e., dually implicative), and its ideal lattice is isomorphic to the filter lattice of $A$ . Moreover, the order dual of the adjoint semilattice is a minimal Brouwerian extension of $A$ , and the...