R(L)弱诱导空间及其连通性

WEAKLY R(L)-INDUCED SPACES AND THEIR CONNECTEDNESS

本文研究了R(L)弱诱导空间的性质及其与R(L)底空间在连通性方面的关系.利用文献[4]中I(L)弱诱导空间引入了R(L)弱诱导空间概念,得到了R(L)弱诱导空间的本质刻划定理.它表明:R(L)弱诱导空间是连通的当且仅当其R(L)底空间是连通的.

The properties of weakly R（L）-induced spaces and the relationship between weakly R（L）-induced spaces and R（L）underlying spaces in connectedness are investigated.Using the concept of weakly I（L）-induced spaces in paper [4],we introduce the concept of weakly R（L）-induced spaces and present a representable theorem of weakly R（L）-induced spaces.The result shows that weakly R（L）-induced spaces are connected iff its R（L）underlying spaces are connected correspondingly.