A point-free relation-algebraic approach to general topology

Abstract

In advanced functional programming, researchers have investigated the existential image, the power transpose, and the power relator, e.g. It will be shown how the existential image is of use when studying continuous mappings between different topologies relationally. Normally, structures are compared using homomorphisms and sometimes isomorphisms. This applies to group homomorphisms, to graph homomorphisms and many more. The technique of comparison for topological structures will be shown to be quite different. Having in mind the cryptomorphic versions of neighborhood topology, open kernel topology, open sets topology, etc., this seems important. Lifting concepts to a relational and, thus, algebraically manipulable and shorthand form, shows that existential and inverse images must here be used for structure comparison. Applying the relational language TituRel to such topological concepts allows to study and also visualize them. © 2014 Springer International Publishing.