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The least extension of a closure operator on a sublattice
- Source :
- Mathematical Proceedings of the Cambridge Philosophical Society. 63:9-10
- Publication Year :
- 1967
- Publisher :
- Cambridge University Press (CUP), 1967.
-
Abstract
- 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 conditionsfor 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.
Details
- ISSN :
- 14698064 and 03050041
- Volume :
- 63
- Database :
- OpenAIRE
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Accession number :
- edsair.doi...........6bc174095efc9bbdf232f8b2f96139ea