  Let $X$ be a locally 1-connected metric space and $A_1,A_2,...,A_n$ be
connected, locally path connected and compact pairwise disjoint subspaces of
$X$. In this paper, we show that the quotient space $X/(A_1,A_2,...,A_n)$
obtained from $X$ by collapsing each of the sets $A_i$'s to a point, is also
locally 1-connected. Moreover, we prove that the induced continuous
homomorphism of quasitopological fundamental groups is surjective. Finally, we
give some applications to find out some properties of the fundamental group of
the quotient space $X/(A_1,A_2,...,A_n)$.
