Some New Completeness Properties in Topological Spaces

Date

2017-06-30

Author

Vural, Çetin
Önal, Süleyman

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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.

URI

https://hdl.handle.net/11511/81707
https://ecommons.udayton.edu/topology_conf/12/

Conference Name

32. Summer Conference on Topology and Its Applications, Dayton / OHIO, Amerika Birleşik Devletleri, 27 Haziran 2017 - 30 Haziran 2016

Collections

Department of Mathematics, Conference / Seminar

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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: https://hdl.handle.net/11511/81707.