A Study on Hyperconnectedness in N -Topological Spaces.

Abstract

In this paper, the notions of Nτ –hyperconnectedness, and Nτ –hyperconnected components have been studied in N-topological spaces, and also extend it to Nτ-pointwise hyperconnectedness in the space. The relation between Nτ –hyper connected spaces and Nτ -pointwise hyperconnectedness has also been examined. With the help of Nτ –hyperconnected components, the dimension of a N -topological space has been obtained, and also a new space, namely Nτ -noetherian space have been studied as an application to Nτ –hyperconnectedness and Nτ –hyperconnected components.