Galois closed subrelations and complete sublattices
by
Klaus Denecke
University of Potsdam, Germany

Galois connections between sets A and B are induced by relations R subset or equal A ×B. To every Galois connection there is associated a pair of closure operators and the fixed points with respect to these closure opeators form two complete lattices which are dually isomorphic. There are several ways to characterize complete sublattices of these complete lattices:

1. by a so-called Galois-closed subrelation R' of the relation R,
2. by a pair of additive closure operators which are conjugate with respect to the relation R,
3. by kernel operators preserving joins,
4. by closure operators preserving meets.

We will describe the first method and the interconnections between 1., 2., 3., and 4.

Date received: March 12, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagi-29.