A Further Discussion On The Separation In L - Fuzzy Topological Spaces

In this paper, we introduce some new separation axioms in L-fuzzy topological spaces by using the pre-open sets, pre-closed sets, pre-closed remote-neighborhoods and pre-continuous functions. Further more,we discuss separation systems in L-fuzzy topological spaces. In L-fuzzy topological spaces, we introduce the concepts of inclusive pre-regular spaces, inclusive pre-normal spaces, complete pre-regular spaces and inclusive completely pre-regular spaces, the generalized Urysohn lemma, and use the generalized Urysohn lemma prove some properties of the above categories of space.Using the same method,we introduce the concepts of inclusive semi-regular spaces, inclusive semi-normal spaces, complete semi-regular spaces and inclusive completely semi-regular spaces.The two kinds of separabilities above do not contain.