2000/02/03 by Roman R. Zapatrin
Mathematics · #math.CT #msc:06A06 #msc:06A15
published as Pure Mathematics and Applications, 9, 485--490 (1998) · latex209, 6 pages
arxiv created 2000/02/03 · arxiv updated 2009/11/30
For an arbitrary partially ordered set P its \em dual P^* is built as the collection of all monotone mappings P→\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^*→\2 preserving universal bounds. Then it is proved that the partially ordered sets P and P** are isomorphic.