On the Decidability of Formulae Involving Continuous and Closed Functions

Abstract

The satisfiability problem for a syllogistic embracing 6, E, Boolean set operations, the Kuratowski topological closure operation, and continuous and closed maps between topological spaces, along with the operations of point evaluation, set image, and inverse set image, is solved for formulae that meet a particular syntactic non-circularity property. The unquantified interpreted language E2 to be considered has infinitely many sorts of variables, each corresponding to a different topological space. Three kinds of variables are available, namely, individual, set, and map variables. Individual variables of a given sort are supposed to range over the universe of that sort, whereas set variables range over the subsets of the appropriate universe. Finally, each map variable ranges over the collection of continuous or closed maps between two appropriate topological spaces.