  By generalizing the whisker topology on the $n$th homotopy group of pointed
space $(X, x_0)$, denoted by $\pi_n^{wh}(X, x_0)$, we show that $\pi_n^{wh}(X,
x_0)$ is a topological group if $n \ge 2$. Also, we present some necessary and
sufficient conditions for $\pi_n^{wh}(X,x_0)$ to be discrete, Hausdorff and
indiscrete. Then we prove that $L_n(X,x_0)$ the natural epimorphic image of the
Hawaiian group $\mathcal{H}_n(X, x_0)$ is equal to the set of all classes of
convergent sequences to the identity in $\pi_n^{wh}(X, x_0)$. As a consequence,
we show that $L_n(X, x_0) \cong L_n(Y, y_0)$ if $\pi_n^{wh}(X, x_0) \cong
\pi_n^{wh}(Y, y_0)$, but the converse does not hold in general, except for some
conditions. Also, we show that on some classes of spaces such as semilocally
$n$-simply connected spaces and $n$-Hawaiian like spaces, the whisker topology
and the topology induced by the compact-open topology of $n$-loop space
coincide. Finally, we show that $n$-SLT paths can transfer $\pi_n^{wh}$ and
hence $L_n$ isomorphically along its points.
