Infimal generators and dualities between complete lattices |
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Authors: | Ivan Singer |
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Institution: | (1) Present address: INCREST, Bdul Pacii 220, 79622 Bucuresti, Romania |
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Abstract: | Summary We give some applications of infimal generators of complete lattices, in the sense of Kutateladze and Rubinov 12], to the study of dualities between two complete lattices E and F (i.e., mappings : E F satisfying
for all
and all index sets I, including the empty set I=Ø). We give some additional results for E=(2X,
), F=(2W,
) and E=(¯RX, ), F=(¯RW, ) (where X and W are arbitrary sets), with suitable families of infimal generators. We obtain some lattice- theoretic properties of the relations of 22] between dualities : (2X,
) (2W,
), binary relations
X×W, polarities (): (2X,
) (2W,
), coupling functionals : X×W ¯R and Fenchel-Moreau conjugations c():(¯RX, ) (¯RW,). |
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Keywords: | |
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