Dedekind Completeness and a Fixed-Point Theorem
- 1 January 1957
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 9, 400-405
- https://doi.org/10.4153/cjm-1957-047-5
Abstract
McShane (5, 6) has introduced the concept of “Dedekind completeness” for partially ordered sets, which seems to be a natural generalization of the usual concept of completeness for lattices. It is the purpose of this paper to discuss some of the properties of Dedekind completeness, particularly with respect to a rather natural class of partially ordered sets which we call “uniform.”Keywords
This publication has 5 references indexed in Scilit:
- A lattice-theoretical fixpoint theorem and its applicationsPacific Journal of Mathematics, 1955
- A characterization of complete latticesPacific Journal of Mathematics, 1955
- Partial Orderings and Moore-Smith LimitsThe American Mathematical Monthly, 1952
- Sur le théorème de ZornArchiv der Mathematik, 1949
- Partially ordered setsTransactions of the American Mathematical Society, 1937