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We know , totally disconnected space and very disconnected topological space is not an important part of the communication space , their concepts are set (X, T) as a topological space , if the right (?) X, y ∈ X, there U, V ∈ T, such that x ∈ U, y ∈ V, and U ∩ V = (?), U ∪ V = X, called (X, T) is totally disconnected space Let (X, T ) as a topological space, if for A (?) X, has Ao-∈ T, called (X, T) is extremely disconnected space Let (Lx, δ) is L- topological space , if ( ? ) xλ, yβ ∈ M * (Lx) , and x ≠ y, (?) U, V ∈ δ, stxλ (?) U, yβ (?) V and U ∧ V = 0, U ∨ V = 1. called (Lx, δ) is totally disconnected space in this paper, the three space constitute the main research object in previous studies based on the topology , this paper from two aspects , one is in distinct topology uses strong semi- open sets on totally disconnected space and extremely disconnected space to study and get a series of conclusions ; hand is given in L-topological concepts totally disconnected space , has been some of its properties , and proves this paper is defined as \introduced before you read this article prior knowledge required in order to describe the content of this third chapter is fully disconnected space some properties in this chapter , gives a totally disconnected space of several equivalent conditions , discuss it with S - totally disconnected relationship between space and transitivity , integrability , etc., and gives a few totally disconnected space conditions for the establishment of Chapter IV pole disconnected space of some properties , this gives a very disconnected space equivalent conditions established by these equivalent conditions extremely disconnected space obtained some properties near and got some extremely disconnected space in the relationship between the collection of the fifth chapter L- topological spaces totally disconnected space definitions and properties in this chapter are given in LF Topological Space totally disconnected space definition and some properties and get it's \
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