Pairwise Connectedness and Pairwise Total Disconnectedness in Bihypertopological Space

Concepts of pairwise separated sets, pairwise connectedness, pairwise disconnectedness and pairwise total disconnectedness for hyperspace of a bitopological space (briefly, called bihypertopological space) are introduced. We obtain some necessary and sufficient conditions under which bihypertopological space is pairwise connected, pairwise disconnected and pairwise totally disconnected. It is proved that pairwise T-1 and pairwise connected bitopological space generates pairwise connected bihypertopological space. It is also proved that bihypertopological space of pairwise totally disconnected bitopological space is also pairwise totally disconnected.