OF FORMULAE INVOLVING CLOSED FUNCTIONS

The satisfiability problem for a syllogistic em­ bracing 6, E, Boolean set operations, the Ku- ratowski topological closure operation ~~, and continuous and closed maps between topologi­ cal spaces, along with the operations of point evaluation, set image, and inverse set image, is solved for formulae that meet a particular syn­ tactic non-circularity property. The unquantified interpreted language £2 to be considered has infinitely many sorts of vari­ ables, each corresponding to a different topo­ logical space. Three kinds of variables are avail­ able, namely, individual, set, and map vari­ ables. Individual variables of a given sort are supposed to range over the universe of that sort, whereas set variables range over the sub­ sets of the appropriate universe. Finally, each map variable ranges over the collection of con­ tinuous or closed maps between two appropri­ ate topological spaces.