On topologized fundamental group and strong small transfer spaces

Rasha Abbas Isewid; Seyed Zeynal Pashaei; Roghayeh Abdi

Rasha Abbas Isewid College of Physical Education and Sports Science, AL-Qadisiyah University, P.O.Box 88, Al-Qadisiyah, Al-Diwaniyah, Iraq.
Seyed Zeynal Pashaei Ferdowsi University of Mashhad
Roghayeh Abdi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751 71379, Iran.

Abstract

?Suppose $H\leq \pi_{1}(X,x_{0})$?. ?In this paper?, ?we show that quotient topological groups are relative strong small loop transfer space which is related to a subgroup of $ \pi_{1}(X,x_{0})$?. ?After?, ?we study the connection between the concepts of semilocally $H$-connected and strong $H$-small loop transfer spaces?. ?finally?, ?we present conditions under which a special generalized covering subgroup is covering?.