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Glukhov, M. M.
Stelletskii, I. V.
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Fofanova, T. S.
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Published online by Cambridge University Press: 24 October 2008
Introduction. We recall (see Morgan Ward (3), Birkhoff (1), p. 49) that a closure operator on a complete lattice ℒ is a mapping f from ℒ into ℒ satisfying the conditions
for all X, Y ∈ ℒ. The set of all closure operators on ℒ is itself a complete lattice with respect to the partial ordering in which f1 ≤ f2 if and only if f1(X) ≥ f2(X) for all X ∈ ℒ for every subset ℱ of
and every element X ∈ ℒ we have
.