Topology + Foundations
32nd Summer Conference on Topology and Its Applications
One of the most widely known completeness property is the completeness of metric spaces and the other one being of a topological space in the sense of Cech. It is well known that a metrizable space X is completely metrizable if and only if X is Cech-complete. One of the generalisations of completeness of metric spaces is subcompactness. It has been established that, for metrizable spaces, subcompactness is equivalent to Cech-completeness. Also the concept of domain representability can be considered as a completeness property. In , Bennett and Lutzer proved that Cech-complete spaces are domain representable. They also proved, in , that subcompact regular spaces are domain representable. Then Fleissner and Yengulalp, in , gave a simplified characterization of domain representability. In this work, we introduce the completeness of a quasi-pair-base and study the topological spaces having such a base. Our results include the fact that Cech-complete spaces and subcompact spaces have complete quasi-pair-basis, and we prove that if a topological space X has a complete quasi-pair-base then X is domain representable.
Copyright © 2017, the Authors
Vural, Cetin and Önal, Süleyman, "Some New Completeness Properties in Topological Spaces" (2017). Summer Conference on Topology and Its Applications. 12.