Connectedness in graded ditopological texture spaces

Abstract

The aim of this paper is to introduce two different types of connectedness notions for graded ditopological texture spaces: the connectedness function which gives the grade of connectedness of a set and the connectedness spectrum by means of spectrum idea. Also, the properties of these connectedness notions and their relationships with the connectedness notion in ditopological case are investigated. Further, the relation between these two different types of connectedness notions is studied.