Topics in Generalized Topology and Fuzzy Generalized Continuities

Abstract

Topics in Generalized Topology and Fuzzy Generalized Continuities This work is comprised of the generalized topology, algebraic generalized topology and fuzzy generalized topology. We have defined and studied the notions of semi- -local function, global function, global closure operator, global interior and -normal spaces in Ideal generalized topological spaces. Properties of these functions are investigated. Examples and counter examples are given where deemed necessary. We continued the investigations of some important results in generalized topological groups and proved basic properties of -connectedness. Along with other results, it is proved that in a -topological group, the maximal -connected components containing the identity of the group is -closed invariant subgroup. -quotients of -topological groups are also discussed. -topological vector spaces (generalization of TVS) are one of the interesting structures which is defined and investigated over here. This space is a blend of -topological structure with the algebraic concept of a vector space in such a way that vector addition and scalar multiplication are -continuous functions. A counter example is given to show that a -topological vector space is not a topological vector space. We have studied the concept of a fuzzy generalized topology which is a generalization of Chang’s fuzzy topology, and investigated some properties of its structure. We have also introduced the concept of fuzzy generalized open function and fuzzy generalized closed function in terms of fuzzy generalized interior and fuzzy generalized closure operators