Continuity as a Galaxy of Hyperreal Functions

Abstract

In the present paper, the problem of defining continuity and scontinuity as a galaxy of hyperreal function is discussed. Our attempt is based on the fact that monads are subsets of some galaxies. New results are obtained, with nonstandard variables, related to a new extension of the continuity notion.

On nonstandard derived numbers of monotonic functions

“…If A is a subset of R 2 , then the monad of A, dented by m(A) is the union of the monads of the points of A [2] and [6].…”

“…If A 1 and A 2 are subset of R 2 , then A 1 and A 2 are called infinitely near, if they have the same monad [2] and [6].…”