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T0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.