与特殊性质P对偶的空间及相关结论

Spaces Which are Dually Special Property P and Related Conclusions

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.

Let X be a space,and P={A∶A is a subset φ of X, and has property P}.A space X is dual the property P if for any neighborhood assignment for X,there is a subset AX,A∈P,such that X=∪{φ(x)∶x∈A}.In this note,we mainly discuss properties of spaces which are dually special P,and also give a necessary and sufficient condition for spaces which are dually special P.These conclusions can be held for many spaces.As a corollary,we have that if X is a regular weak θ-refinable(dually discrete)-scattered space,then X is d...