Borel measures in consonant spaces
Borel measures in consonant spaces
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DOI：
10.1016/0166-8641(95)00089-5
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发表时间：
1996-06
影响因子：
0.6
通讯作者：
A. Bouziad
中科院分区：
文献类型：
--
作者：
A. Bouziad
一个集合X上的拓扑T称为协和的，如果格T的Scott拓扑是紧生成的;等价地，如果X的闭集上的上Kuratowski拓扑和余紧拓扑重合。证明了每个完全正则辅音空间都是Prohorov空间，每个第一可数正则辅音空间都是遗传Baire空间。如果X是可度量化可分的和共解析的，则X是辅音的当且仅当X是波兰语的。最后，我们证明了每个伪紧拓扑群只要是和谐的，就一定是紧的。Dolecki，Greco和Lechicki，Nogura和Shakmatov的几个问题得到了解决。
A topology T on a set X is called consonant if the Scott topology of the lattice T is compactly generated; equivalently, if the upper Kuratowski topology and the co-compact topology on closed sets of X coincide. It is proved that every completely regular consonant space is a Prohorov space, and that every first countable regular consonant space is hereditarily Baire. If X is metrizable separable and co-analytic, then X is consonant if and only if X is Polish. Finally, we prove that every pseudocompact topological group which is consonant is compact. Several problems of Dolecki, Greco and Lechicki, of Nogura and Shakmatov, are solved.