几种类型局部紧空间及其性质

Several kinds of locally compact spaces and their natures

给出了几种类型的局部紧空间:局部可数紧空间,邻域局部紧空间,局部序列紧空间,局部列紧空间,并且研究了它们的拓扑性质,有限可积性,遗传性,得到的主要结果是:局部可数紧和邻域局部紧性是拓扑不变性,有限可积性;局部序列紧是拓扑不变性,同时满足闭可遗传性等一些性质.

In this article we study some kinds of locally compact space,locally neighbourhood compact space,locally sequent compact space ,locaUy bicompact space and discuss their topological property,hereditary property, finite product property. And we achieve some results：locally countably compactness, locally neighbourhood compactness are topological invariance, finite product property;locally sequent compactness is topological invariance and closed hereditary property.