  In this paper we show that the nth quasitopological homotopy group of a
topological space is isomorphic to (n-1)th quasitopological homotopy group of
its loop space and by this fact we obtain some results about quasitopological
homotopy groups. Finally, using the long exact sequence of a based pair and a
fibration in qTop introduced by Brazas in 2013, we obtain some results in this
field.
