Fuzzy Absolutes and Related Topics

Abstract

The study on the fuzzy absolutes and related topics. The different kinds of extensions especially compactification formed a major area of study in topology. Perfect continuous mappings always preserve certain topological properties. The concept of Fuzzy sets introduced by the American Cyberneticist L. A Zadeh started a revolution in every branch of knowledge and in particular in every branch of mathematics. Fuzziness is a kind of uncertainty and uncertainty of a symbol lies in the lack of well-defined boundaries of the set of objects to which this symbol belongs. Introduce an s-continuous mapping from a topological space to a fuzzy topological space and prove that the image of an H-closed space under an s-continuous mapping is f-H closed. Here also proved that the arbitrary product fi and sum of  fi of the s-continuous maps fi are also s-continuous. The original motivation behind the study of absolutes was the problem of characterizing the projective objects in the category of compact spaces and continuous functions.