Nonstandard Topology on R

Abstract

Nonstandard topology on is a kind of topology constructed by means of nonstandard analysis on . The ordered field of nonstandard real numbers (or simply hyperreals) has been introduced. It extends the reals . The hyperreals properties and the main topological definitions for with the standard topology have been presented in the nonstandard context. Nonstandard proofs of well-known theorems from the topology on have been given and compared with the standard ones. Keywords Ultrapower, Hyperreals, Transfer Principle, (Nonstandard) Topology on .