p-仿紧空间和局部p-仿紧空间

On p-paracompact spaces and locally p-paracompact spaces

目的利用预开集引入p-仿紧空间和3种局部p-仿紧空间的定义并研究它们的性质。方法利用逻辑推理的证明方法。结果与结论得到了p-仿紧空间和3种局部p-仿紧空间的遗传性质、映射性质、乘积性质、拓扑和性质和分离性质等,丰富了p-仿紧空间的某些理论。

Objective-To introduce the concepts of p-paracompact spaces and the three kinds of lo cally p-paracompact spaces with preopen sets and investigate their properties. Methods--Logical rea soning is used to prove the aforesaid conditions. Results and Conclusion-The heritability properties, mapping properties, product properties, topological sum properties, separation properties of p-para compact spaces and the three kinds of locally p-paracompact spaces are obtained, and some theories on p-paracompact spaces are enriched.