| As we kown, the concept of complete unconnected space and extremally unconnected space is well kown as follow:(X,T) is an topology space, if every x, y∈X,(?)U,V∈T, s.t. x∈U, y∈V, U∩V=(?) and U∪V=X, (X,T) is called an complete unconnected space.(X,T) is an topology space, if every A(?)X, A(?)∈T, (X,T) is called an extremally unconnected space.(Lx,δ) is an L-topology space, if every xλ, yβ∈M*(Lx),x≠y, (?)U, V∈δ,s.t. xλ(?) U,yβ(?) V,and U∧V=0,U∨V= 1,(LX,δ) is called an complete unconnected space.In this paper, those three unconnected spaces have been discussed as the main items. Basing on the former research, on one hand, this paper used the strong semi-open sets to discuss the complete unconnected space and extremally unconnected space; on the other hand, the concept of complete unconnected space is given in the L-Topology and some characters about complete unconnected space are given in the L-Topology.Chapter One is introduction. The main idea in this chapter is introduced something about my research field in the topology, such as the emergence of topology in my research field and its development.Chapter Two is preliminaries. There are two parts in this chapter: one is definitions and the other is theorems. Those definitions and theorems will be helpful for readers.Chapter Three is obtained the equivalent of the complete unconnected space, and discussed the relationship with the S-complete unconnected space, and the characters about integrable,transferable and so on. At the same time, some conditions are given in this paper which make a space become a complete unconnected space. Chapter Four Some equivalent conditions of the extremally disconnected space are given in this paper. According to those equivalent conditions, some good characters of the extremally disconnected space is presented, then, some relationship about sets in extremally disconnected space is given in this chapter.Chapter Five, the concept of L-complete unconnected spaces has been given, and it is a L-good extension.
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