正则空间 meaning in English
regular space
Examples
- Completely regular space
完全正则空间 - On its basis , gao zhimin introduced the concept of pair - network and proved that a space has - locally finite pair - networks if and only if it is cosmic space in 1986
在此基础上， 1986年高智民引入了双网络( pair - network )的概念，证明了具有局部有限双网络的正则空间等价于cosmic空间。 - In other words , d . burke and r . engelking and d . lutzer proved that a regular space is metrizable space if and only if it has a - hereditarily closure - preserving base in 1975 , and introduced weakly hereditarily closure - preserving families , which proved that a regular k - space has - weakly hereditarily x closure - preserving bases is metrizable space , too
Burke ， r engelking和d lutzer证明了正则空间是可度量化空间当且仅当它具有遗传闭包保持基，并引入了弱遗传闭包保持集族( weaklyhereditarilyclosure - preservingfamilies ) ，同时证明了具有弱遗传闭包保持基的正则的k空间是可度量化空间。 - Yan pengfei proved that a space has point countable pair - networks if and only if it is cosmic space in 1999 further and put forword the question how we depict the space with - hereditarily closure - preserving pair - networks on the basis of acquirement of interested characteristics of the space with - hereditarily closure - preserving cs * - networks
1999年燕鹏飞进一步证明了具有点可数双网络的正则空间也等价于cosmic空间，并在获得了具有遗传闭包保持cs ~ *双网络( cs ~ * - network )空间的有趣的内在特征之后提出问题：如何刻画具有遗传闭包保持双网络的正则空间 - The paper has four parts . the first chapter , introduction , gives the origin of the problems and our main results . the second chapter proves that countable paracompact ( mesocompact , metacompact ) spaces have the characterization of junnila ' s and that hereditarily mesocompact spaces do n ' t have it . at last , we give the sufficient conditions for a space having the property that its every scattered partition has a compact - finite open expansion
第二章详细证明了可数仿紧(中紧、亚紧)空间有类似junnila的刻画，遗传中紧空间不具有类似junnila的刻画，最后给出了正则空间的每个散射分解有紧有限的开膨胀的充要条。