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bu fen ming tychonoff kong jian
Author(s): 
Pages: 1-4
Year: Issue:  3
Journal: Acta Scientiarum Naturalium Universitatis Neimongol

Keyword:  不分明拓扑空间完全正则子空间不分明集不分明单位区间定理充分必要条件乘积相对拓扑当且仅当;
Abstract: <正> 设I=[0,1],它在数直线中的相对拓扑记为,我们称乘积诱导不分明拓扑空间(I,Fθ×θI为乘积诱导不分明单位区间,记为ω[0,1]。定义1 不分明拓扑空间(X,F)叫做不分明完全正则的,当且仅当对任一不分明开集A∈F和任一点Px0α∈A,都有一个不分明连续映像T:(X,F)→ω[0,1],使得T(x0)=0,T[X~~υα(A)]={1}。这里υα(A)=U{U:Px0α∈NUβA},NUβ是点Px0α的邻域胚。不难看出,当α<1时,对任何A∈F都有υα(A)=σα(A),即A的强α—截割。定理1 若不分明拓扑空间(X,F)是不分明完全正则的,则它一定是拓扑生成的,也就
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