Some Results in Quasitopological Homotopy Groups

Abstract

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