Many Theories And Application Of The Nonstandard Analysis In Topology

In this paper, we use the saturated model and enlargement model study the topology space, give nonstandard characters of some notions, such as sober space, separations, net and universal net etc.In the first part, we introduce the nonstandard analysis theory simply. Using the axioms in nonstandard analysis give the nonstandard model and discuss some properties of nonstandard model.In the second part, we use theory of nonstandard analysis theory discuss the notion, nonstandard compactifications and separations in topology .In the processing of applications, some relative theorems and results are proved.Through the research of this paper, on the one hand, it makes the theory and the practice a more perfect union, and enhances us to get more widespread understanding to the subject about nonstandard analysis. On the other hand, it makes the theory of nonstandard analysis richer, and is helpful to the development of nonstandard analysis in other applied domains.