Non-additive closures and function spaces
by
Eva Colebunders
Vrije Universiteit Brussel
Coauthors: V. Claes, G. Sonck

In the construct CLS objects are sets, structured by a non- additive closure operator and morphisms are continuous functions, i.e. they preserve the closure. Sometimes CLS is described in an isomorphic way, via collections of closed sets, so called Moore families. Non- additive closures have been considered for instance in relation with lattice theory and with projective geometry. Not only within mathematics, but also in mathematical models for social sciences or in the foundations of physics, non- additive closures arise very naturally.

It is known that the construct CLS is a topological construct. In our talk we will discuss other convenience properties, such as the existence of nice function spaces. In the setting of CLS products of quotients are quotients, but on the other hand products do not distribute over coproducts. So CLS is not Cartesian closed and moreover we prove that exponential objects in CLS are indiscrete. We construct a Cartesian closed topological superconstruct of CLS and we characterize the objects in the Cartesian closed topological hull.

Date received: June 21, 2000

Copyright © 2000 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 # caeq-49.