ABSTRACT
Beside using nonstandard analysis as independently developed field of
mathematics in general and especially in mathematical Analysis, the using of
nonstandard as techniques have more powerful for introducing and developing
different concepts in mathematics.
In this thesis, we use some concepts of nonstandard analysis given by
A. Robinson, (Robinson, 1974) and axiomatized by E. Nelson, (Nelson, 1977)
to reprove some classical results of Compactness by using the nonstandard
tools and get some new results. Also, we introduce a nonstandard definition of
quasi-metric spaces and quasi-compactness and generalizing these concepts to
be valid for external sets.
