Structure Results for Function Lattices
Open Access
- 1 April 1978
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 30 (2) , 392-400
- https://doi.org/10.4153/cjm-1978-034-1
Abstract
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.Keywords
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