On Fixed Edges of Antitone Self-mappings of Complete Lattices
Publications de l'Institut Mathématique, _N_S_34 (1983) no. 48, p. 49
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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.
Klimeš'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 :
06A10
Rade M. Dacić. On Fixed Edges of Antitone Self-mappings of Complete Lattices. Publications de l'Institut Mathématique, _N_S_34 (1983) no. 48, p. 49 . http://geodesic.mathdoc.fr/item/PIM_1983_N_S_34_48_a7/
@article{PIM_1983_N_S_34_48_a7,
author = {Rade M. Daci\'c},
title = {On {Fixed} {Edges} of {Antitone} {Self-mappings} of {Complete} {Lattices}},
journal = {Publications de l'Institut Math\'ematique},
pages = {49 },
year = {1983},
volume = {_N_S_34},
number = {48},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1983_N_S_34_48_a7/}
}