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Completeness in Semi-Lattices

Published online by Cambridge University Press:  20 November 2018

L. E. Ward Jr.
L. E. Ward Jr.*
Affiliation:
U.S. Naval Ordnance Test Station China Lake, California
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Let (X, ≤) be a partially ordered set, that is, X is a set and ≤ is a reflexive, anti-symmetric, transitive, binary relation on X.

We write

,

for each x ∈ X. If, moreover,

exists for each x and y in X, then (X, ≤) is said to be a semi-lattice.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 578 - 582
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Alexander, J. W., Ordered sets, complexes, and the problem of bicompactification, Proc. Nat. Acad. Sci., 25 (1939), 296–298.Google Scholar
2. Birkhoff, Garrett, Lattice Theory (rev. ed., New York, 1948).Google Scholar
3. Davis, Anne C., A characterization of complete lattices, Pacific J. of Math., 5 (1955), 311–319.Google Scholar
4. Frink, O., Topology in lattices, Trans. Amer. Math. Soc. 51 (1942), 569–582.Google Scholar
5. Tarski, Alfred, A lattice-theoretical fixpoint theorem and its applications, Pacific J. of Math., 5 (1955), 285–309.Google Scholar
6. Ward, L. E., Partially ordered topological spaces, Proc. Amer. Math. Soc. 5 (1954), 144–161.Google Scholar