Algebraic duality for partially ordered sets

Details Algebraic duality for partially ordered sets Algebraic duality for partially ordered sets

2000-02-03

arxiv.org/abs/math/0002025v1

Pure Mathematics and Applications, 9, 485--490 (1998)

Mathematics

Category Theory

latex209, 6 pages

Scientific paper

For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the pointwise partial order. The {\em second dual} $P^{**}$ is built as the collection of all morphisms of complete lattices $P^*\to\2$ preserving universal bounds. Then it is proved that the partially ordered sets $P$ and $P^{**}$ are isomorphic.

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