Closed set logic in categories / William James.

Abstract

This thesis investigates two related aspects of a dualisation program for the intuitionist logic in categories. The dualisation program has as its end the presentation of closed set logic in place of the usual open set logic found in association with toposes. The study is concerned especially with Brouwerian algebras in categories as the duals of the usual Heyting algebras. Defines the notion of a sheaf over the closed sets of a topological space. Investigates the sheaves for their algebric properties in relation to base space topologies.