Some New Completeness Properties in Topological Spaces

Vural, Çetin
Önal, Süleyman
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 [1], Bennett and Lutzer proved that Cech-complete spaces are domain representable. They also proved, in [2], that subcompact regular spaces are domain representable. Then Fleissner and Yengulalp, in [3], 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.
32. Summer Conference on Topology and Its Applications, Dayton / OHIO, Amerika Birleşik Devletleri, 27 Haziran 2017 - 30 Haziran 2016


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Citation Formats
Ç. Vural and S. Önal, “Some New Completeness Properties in Topological Spaces,” presented at the 32. Summer Conference on Topology and Its Applications, Dayton / OHIO, Amerika Birleşik Devletleri, 27 Haziran 2017 - 30 Haziran 2016, Dayton / OHIO, Amerika Birleşik Devletleri, 2017, Accessed: 00, 2021. [Online]. Available: