Intuitionistic Topology

Abstract

This thesis titled INTUITIONISTIC TOPOLOGY, is Proving the 177 theorems of General Topology by a newly introduced Intuitionistic Logic named as BHUVANA RAMYA INTUITIONISTIC LOGIC, (shortly BRIL). In this thesis a new logic BRIL has been introduced in an intuitionistic way. That new logic BRIL will work as an Effective Theorem Prover. BRIL can be applied to prove any kind of non declarative (sometimes, declarative too) compound statements of any subject, just by mental activity. Few theorems of various subjects/branches of a subject are proved using BRIL to make this statement True. Our newly introduced logic BRIL contradicts with the Aristotle s sayings that No statement is both true and false; that is, BRIL rejects the Aristotelian Law of Excluded Middle. That s why BRIL is called as an Intuitionistic Logic. In this thesis, it is also proved that the theorems proven by BRIL cannot be proved by Classical Constructivism. newline