L-拓扑空间中的*-拟仿紧性

利用α-正则闭远域族在L-拓扑空间中定义了一种新的仿紧性,即*-拟仿紧性,并用半内部对其进行了刻划。研究了*-拟仿紧性所具有的一些性质,比如L-good extension,正则闭遗传,弱同胚不变性。讨论了*-拟仿紧空间的半正则化以及*-拟仿紧性在诱导空间中的重要性质。

*-Nearly paracompactness in L-topological spaces

With α-regular closed remote family, a new paracompactness called *-nearly paracompactness in L-topological spaces was introduced, and was characterized by means of semi-interior. It was proved that *-nearly paracompactness has many properties,such as that it has L-good extension,hereditary with respect to regular closed subsets and weakly in homeomorphic invariant property. Also, the semi-regularization space of *-nearly paracompactness was discussed, the importantproperties of *-nearly paracompactness in induced space were also obtained.