Z-compact, The Z-countably Compact And The Z-lindel (?) F L-fuzzy, Set

The concept of fuzzy topological space was introduced by C.L.Chang in 1968 under the theory of fuzzy sets. At the same time the open sets, the closed sets, the neighborhoods, the Compactness, the countably compactness and the connectedness were introduced. After that same researches extended the properties to the general L-fuzzy topological spaces. In this paper we have introduced a kind of new open sets and had discussed the Z-compactness, Z-type of strong connectedness, countably Z-compactness, Z-Lindel(o|¨)f properties, and SP-Urysohn space, it preserves many good properties.The first chapter we lay out some basic knowledge including some results which will be used later. In the second chapter, we introduce many new kinds of nearly open sets in L-fts, discuss its basic properties. In the third chapter, we shall systematically discuss Z-compactness,countably Z-compactness and Z-Lindelof properties. They can be characterized in term ofα-net,α-filter, r-Z-covers and r~+-finite intersection property. In the forth chapter, we shall introduce a new type of connectedness, introduce Z-type of strong connectedness, discuss its properties, and study its relation with other type of connectedness. In the fifth chapter, we also introduced the concept of sp-Urysohn space in L-fuzzy topological spaces, establish some of its fundamental properties, and study their structure relations with known many kind of Urysohn spaces.