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Free Lattices Generated by Partially Ordered Sets and Preserving Bounds

Published online by Cambridge University Press:  20 November 2018

R. A. Dean
R. A. Dean*
Affiliation:
California Institute of Technology Pasadena, California
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A construction of the free lattice generated by a partially ordered set P and preserving every least upper bound (lub) and greatest lower bound (glb) of pairs of elements existing in P has been given by Dilworth (2, pp. 124-129) and, when P is finite, by Gluhov (5).

The results presented here construct the free lattice FL generated by the partially ordered set P and preserving

(1) the ordering of P

(2) those lub's of a family of finite subsets of P which possess lub's in P

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 136 - 148
Copyright
Copyright © Canadian Mathematical Society 1964

References

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