Nonstandard Analysis Methods for Separations in [0, 1]-Topological Spaces (Communications in Mathematical Research, 2021)
In nonstandard enlargement, the separations are characterized by nonstandard analysis methods in [0, 1]-topological spaces. Firstly, the monads of fuzzypoint 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 separationsare investigated.
Keywords: nonstandard enlargement; fuzzy point; [0; 1]-topological space; remote-neighborhood; monad.