Let H be a subgroup of the fundamental group Ο1β(X,x0β). By
extending the concept of strong SLT space to a relative version with respect to
H, strong H-SLT space, first, we investigate the existence of a covering
map for strong H-SLT spaces. Moreover, we show that a semicovering map is a
covering map in the presence of strong H-SLT property. Second, we present
conditions under which the whisker topology agrees with the lasso topology on
XHβ. Also, we study the relationship between open subsets of
Ο1whβ(X,x0β) and Ο1lβ(X,x0β). Finally, we give some
examples to justify the definition and study of strong H-SLT spaces.Comment: 16 page