Algebraic duality for partially ordered sets

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dc.creatorZapatrin, Roman R.
dc.date2000-02-03
dc.date.accessioned2026-07-07T04:33:34Z
dc.date.available2026-07-07T04:33:34Z
dc.descriptionFor 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.
dc.descriptionlatex209, 6 pages
dc.identifierhttps://arxiv.org/abs/math/0002025
dc.identifierhttp://arxiv.org/abs/math/0002025
dc.identifierPure Mathematics and Applications, 9, 485--490 (1998)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58623
dc.subjectCategory Theory
dc.subject06A06; 06A15
dc.titleAlgebraic duality for partially ordered sets
dc.typetext

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