# Some results in quasitopological homotopy groups

## TL;DR

This paper explores properties of quasitopological homotopy groups, establishing isomorphisms with loop space groups and deriving new results using exact sequences and fibrations.

## Contribution

It demonstrates that the nth quasitopological homotopy group is isomorphic to the (n-1)th group of the loop space and applies exact sequences to derive new insights.

## Key findings

- Isomorphism between nth quasitopological homotopy group and (n-1)th of loop space
- Derived new results using long exact sequences and fibrations in qTop
- Extended understanding of quasitopological homotopy groups

## Abstract

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.