WHEN DO THE UPPER KURATOWSKI TOPOLOGY (HOMEOMORPHICALLY, SCOTT TOPOLOGY) AND THE CO-COMPACT TOPOLOGY COINCIDE

摘要

A topology is called consonant if the corresponding upper Kuratowski topology on closed sets coincides with the co-compact topology, equivalently if each Scott open set is compactly generated. It is proved that Cech-complete topologies are consonant and that consonance is not preserved by passage to G(delta)-sets, quotient maps and finite products. However, in the class of the regular spaces, the product of a consonant topology and of a locally compact topology is consonant. The latter fact enables us to characterize the topologies generated by some Gamma-convergences. [References: 23]