R(L$型诱导空间的分离性和良紧性

The Separation and $N$-Compactness of Induced $R(L)$-Fuzzy Topological Spaces

中文关键词:  R(L)型诱导空间  分离性  良紧性.

英文关键词:Induced $R(L)$-fuzzy topological spaces  separation  $N$-compactness.

中文摘要:

      本文给出了$LF$拓扑空间$(L^X,\delta)$具有各级分离性等价于其$R(L)$型诱导空间$(R(L)^X,\omega(\delta))$具有相应的性质.证明了$(L^X,\delta)$是良紧空间当且仅当$(R(L)^X,\omega(\delta))$是良紧空间.

英文摘要:

      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.