| In this paper, we prove that $(L^X,\delta)$ is $T_0,T_1,T_2$, regular ($T_3$), normal ($T_4$) and completely regular spaces if and only if $(R(L)^X,\omega(\delta))$ is $T_0, T_1, T_2$, regular ($T_3$), normal ($T_4$) and completely regular spaces, respectively, and $(L^X,\delta)$ is $N$-compact if and only if $(R(L)^X,\omega(\delta))$ is $N$-compact. |
