EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 34(48), pp. 49--53 (1983)

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ON FIXED EDGES OF ANTITONE SELF-MAPPINGS OF COMPLETE LATTICES

Rade M. Daci\'c

Matematicki institut SANU, Beograd, Yugoslavia

Abstract: Studying fixed edges we start from a more general notion---p-pairs and p-points proving first that the set of all p-points of an antitone self-mapping of a complete lattice $L$ is a sublattice of $L$. In this way we obtain as a direct consequence J. Klimes's Fixed edge Theorem and provide an easy proof of his Theorem 2. Besides, this approach sheds much more light on the treated problems. In the sequel (Theorem 2) we examine under which conditions a distinguished pair $(s,t)$ (see Notation) appearing in inconditionally complete posets is a fixed edge. In Theorem 3 the Problem in the text is solved in a special case.

Classification (MSC2000): 06A10

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Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
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