Abstract
An arbitrary partially ordered set P and an isotone mappingϕ of this set into a complete lattice L are considered. It is proved that the mappingϕ can be extended to an isotone mappingϕ of the lattice FL(P) into the lattice L.
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R. A. Dean, “Free lattices generated by partially ordered sets and preserving bounds,” Canad. J. Math.,16, No. 1, 136–148 (1964).
Yu. I. Sorkin, “Free unions of lattices,” Matem. Sb.,30, 677–694 (1952).
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Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 405–416, October, 1968.
The author is deeply indebted to L. A. Skornyakov, under whose guidance the work has been done.
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Fofanova, T.S. Isotone mapping of free lattices. Mathematical Notes of the Academy of Sciences of the USSR 4, 734–741 (1968). https://doi.org/10.1007/BF01093711
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DOI: https://doi.org/10.1007/BF01093711