Extending the Topological Interpretation to Intuitionistic Analysis, II

Publisher Summary This chapter focusses on extending the topological interpretation to intuitionistic analysis. The universally quantified three-variable consequences of the axioms of order have been discussed. A universal sentence is a consequence in Heyting's predicate calculus (HPC) of a given universal axiom if its matrix is a propositional consequence of a finite number of substitution instances of the axiom using the variables. The chapter discusses the general metamathematical implications for the theory of the topological model of intuitionistic analysis. The chapter discusses the important step that is taken for enlarging the model to encompass arbitrary (extensional) real functions. The main result is the verification in the model of Brouwer's theorem on continuity: all functions are uniformly continuous on closed intervals.