Biclosed Binary Relations and Galois Connections.

Abstract

Given two closure spaces (E,j) and (E',j'), a relation R inclue dans E x E' is said biclosed if every row of its matrix representation corresponds t o a closed subset of E', and every column to a closed subset of E. An isomorphism between, on the one hand, the set of all biclosed relations and, on the other hand, the set of all Galois connections between the two lattices of closed sets is established. Several computational applications are derived from this result.DATA ANALYSIS ; MATHEMATICS ; CONNECTIONS