θ-复形的图结构

The Graph Structure of θ- complex

给出了一类特殊拓扑空间—θ-复形和θ-复形的图的定义,然后讨论了θ-复形的图结构,从而更加形象直观地描述了θ-复形中顶点、开滤子与闭滤子之间的关系,并证明了结论:(1)设K是θ-复形,G为其图,则对任意的中心滤子点U,有2≤d G(U)≤3;(2)设K是θ-复形,G为其图,则在G中不存在循环图;(3)设θ-复形K的图G为树,则在G中任意两个中心滤子点均由唯一的途径连接;(4)设u为中心滤子点,v为边滤子点或者顶点,则有d(u,v)=2m-1,m∈ω.

This paper first introduces a specific topological space--θ - complex, and gives the definition of θ - complex＇ s graph. The graph structure of θ - complex is discussed, in order to describe the relations between vertex, open filter and closed filter more directly and visually. The following results are proved： （1） Let K be a θ - complex and its graph G, then for each central filter point U, 2 ≤ dG （U） ≤ 3 ; （2） Let K be a θ - complex and its graph G, then there is no cyclic graph in G;（3） Let be a θ- complex and its graph G, then any two central filter point can be joined by the only way in G; （4） Let u be a central filter point, v be a limbic filter point or vertex ,then d（ u ,v） = 2m - 1 ,m ∈ω.