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Structure Results for Function Lattices

Published online by Cambridge University Press:  20 November 2018

D. Duffus ,
B. Jónsson  and
I. Rival
D. Duffus
Affiliation:
University of Calgary Calgary, Alberta
B. Jónsson
Affiliation:
University of Calgary Calgary, Alberta
I. Rival
Affiliation:
Vanderbilt University Nashville, Tennessee
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For partially ordered sets X and F let Yx denote the set of all order-preserving maps of X to Y partially ordered by f ≦ g if and only if f(x)≦ g (x) for each x ∈ X [1; 4; 6]. If X is unordered then Yx is the usual direct product of partially ordered sets, while if both X and Y are finite unordered sets then Yx is the commonplace exponent of cardinal numbers. This generalized exponentiation has an important vindication especially for those partially ordered sets that are lattices.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 392 - 400
Copyright
Copyright © Canadian Mathematical Society 1978

References

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