Nonstandard Analysis Methods for Separations in [0, 1]-Topological Spaces

Abstract

In nonstandard enlargement, the separations are characterized by nonstandard analysis methods in [0, 1]-topological spaces. Firstly, the monads of fuzzy point in [0, 1]-topological spaces are described with remote-neighborhoods in nonstandard enlarged model. Then the nonstandard characterizations of separations in [0, 1]-topological space are given by the monads. At last, relations of these separations are investigated.