Some strong forms of connectedness in topological spaces.

In this paper, we study new separations of sets called half separated, half β-separated, half semi-separated, half pre-separated, half β-separated sets and corresponding to these notions introduced half connected, half β-connected, half semi-connected, half pre-connected, half β-connected topological spaces, respectively. These are stronger forms of connectedness, β-connectedness, semi-connectedness, pre-connectedness, β- connectedness respectively. The properties of these notions follow the same pattern. [ABSTRACT FROM AUTHOR]