INTERVAL-VALUED SMOOTH TOPOLOGICAL SPACES

Abstract

We list two kinds of gradation of openness and we study in the sense of the followings: (i) We give the definition of IVGO of fuzzy sets and obtain some basic results. (ii) We give the definition of interval-valued gradation of clopeness and obtain some properties. (iii) We give the definition of a subspace of an interval-valued smooth topological space and obtain some properties. (iv) We investigate some properties of gradation preserving (in short, IVGP) mappings.