The Separation and $N$-Compactness of Induced $R(L)$-Fuzzy Topological Spaces
Received:September 27, 2006  Revised:July 13, 2007
Key Word: Induced $R(L)$-fuzzy topological spaces   separation   $N$-compactness.
Fund ProjectL:the National Natural Science Foundation of China (No.10471083); the Natural Science Foundation of Zhejiang Education Committee (No.20060500).
 Author Name Affiliation LIU Zhi Bin College of Mathematics and Physics, Zhejiang Normal University, Zhejiang 321004, China
Hits: 11731
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.