Nonstandard topology on R

الملخص EN

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 wellknown theorems from the topology on have been given and compared with the standard ones.