Some results in quasitopological homotopy groups

T.  Nasri; H. Mirebrahimi; H. Torabi

doi:10.37863/umzh.v72i12.564

T. Nasri Dep. Pure Math., Faculty Basic Sci., Univ. Bojnord, Iran
H. Mirebrahimi Dep. Pure Math., Center Excellence in Analysis on Algebraic Structures, Ferdowsi Univ. Mashhad, Iran
H. Torabi Dep. Pure Math., Center Excellence in Analysis on Algebraic Structures, Ferdowsi Univ. Mashhad, Iran

DOI: https://doi.org/10.37863/umzh.v72i12.564

Keywords: Homotopy group, Quasitopological group, Fibration

Abstract

UDC 515.4

We show that the $n$th 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.

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