Document Type
Topology + Foundations
Publication Date
6-2017
Publication Source
32nd Summer Conference on Topology and Its Applications
Abstract
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.
Copyright
Copyright © 2017, the Authors
eCommons Citation
Vural, Cetin and Önal, Süleyman, "Some New Completeness Properties in Topological Spaces" (2017). Summer Conference on Topology and Its Applications. 12.
https://ecommons.udayton.edu/topology_conf/12
Comments
This document is available for download with the permission of the presenting author and the organizers of the conference. Permission documentation is on file.
Technological limitations may prevent some mathematical symbols and functions from displaying correctly in this record’s metadata fields. Please refer to the attached PDF for the correct display.