L-Fuzzy H-分离性

L-Fuzzy H-Separation

引入了 θ-拓扑空间的概念 ,得到一个有意义的结果是关于诱导 LF拓扑空间的 θ-拓扑与原空间的 θ-拓扑的诱导 LF拓扑之间的关系 :ωL( Tθ) =( ωL( T) ) θ,作者研究了 H- T2 、Hutton正则、几乎 Hutton正则等空间的一些性质 ,回答了文献 [1 ]中提出的一个公开问题。

The notion of θ topological space is introdoced in LF topological space,and a new separation,i.e. H T 2 separation is defined in LF topological spaces.H T 2 is equivalent to T 2 in crisp spaces but different from T 2 in LF topological spaces.The main results are that:For every crisp space ( X,T ) and its induced LF topological space( L x,ω L(T) ),then ω L(T θ)=(ω L(T)) θ,ω L(T S)=(ω L(T)) S, where T S and (ω L(T)) S are respectively semi regularization topological spaces in respect to ( X,T ) and (L X,ω L(T)) ; H T 2 separation is hereditary and productive.It is a semi regular property and an L good extension; Hutton regularity is hereditary and productive and is an L good extensioin; Almost Hutton regularity is a semi regular property and an L good extension; In crisp topological spaces. S regularity is productive.This result gives a positive answer to the open question put forward by Hu Qingping [1] in J.Math.Res.Exp.(1984),i.e. whether S regularity (in crisp spaces)is productive or not.