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与特殊性质P对偶的空间及相关结论

Keywords: 弱θ-加细空间,aD-空间,对偶,D-空间

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Abstract:

X是拓扑空间,令P={A∶A是X的具有性质P的子集},如果对于X的任意邻域指派,都存在A∈P,使得X=∪{(x)∶x∈A},则称X是与性质P对偶的空间.对于给定的特殊性质P,主要讨论了与性质P对偶的空间的一些基本性质,并给出了X是与性质P对偶空间的充分必要条件.这些结论可应用于多种空间类,作为其中的一推论,得到每个正则弱θ-加细(离散对偶)-散布空间是离散对偶空间.另外,还讨论了aD-空间的相关结论.

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