摘要
本文主要讨论局部强紧空间的性质,特别是其Hoare空间和Smyth空间的性质,证明了T_0空间为局部强紧空间的当且仅当其Hoare空间为局部强紧空间,局部强紧空间的Smyth空间为C-空间.对于强局部紧空间,我们有类似的结论.
In this paper, we discuss some properties of locally strongly compact spaces, especially the properties of their Hoare spaces and Smyth spaces. It is proved that a To space is locally strongly compact if and only if its Hoare space is locally strongly com- pact and the Smyth space of a locally strongly compact space is a C-space. Analogous results are obtained for strongly locally compact spaces.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2010年第5期989-996,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(10331010
10861007)
高等学校全国优秀博士学位论文作者专项资金(2007B14)
江西省自然科学基金(2007GZS0179
2009GZS0012)
江西省教育厅基金(GTT08162)资助项目
关键词
局部强紧空间
C-空间
超连续格
locally strongly compact space
C-space
hypercontinuous lattice
