Document Type : Research Paper
Department of Mathematics, College of Education for Pure Sciences (Ibn Al-Haitham), Baghdad University, Baghdad, Iraq
The main purpose of this paper is to introduce a some concepts in fibrewise totally topological space which are called fibrewise totally mapping, fiberwise totally closed mapping, fibrewise weakly totally closed mapping, fibrewise totally perfect mapping fibrewise almost totally perfect mapping. Also the concepts as totally adherent point, filter, filter base, totally converges to a subset, totally directed toward a set, totally rigid, totally-H-set, totally Urysohn space, locally totally-QHC totally topological space are introduced and the main concept in this paper is fibrewise totally perfect mapping in totally topological space. Several theorem and characterizations concerning with these concepts are studied.