Compact complement topologies and k-spaces
Authors:
- K. Keremedis,
- C. Özel,
- A. Piękosz,
- M. A. Al Shumrani,
- E. Wajch
Abstract
Let (X,τ) be a Hausdorff space, where X is an infinite set. The compact complement topology τ? on X is defined by: τ? = {∅}∪{X\M: M is compact in (X,τ)}. In this paper, properties of the space (X,τ?) are studied in ZF and applied to a characterization of k-spaces, to the Sorgenfrey line, to some statements independent of ZF, as well as to partial topologies that are among Delfs-Knebusch generalized topologies. Between other results, it is proved that the axiom of countable multiple choice (CMC) is equivalent with each of the following two sentences: (i) every Hausdorff first-countable space is a k-space, (ii) every metrizable space is a k-space. A ZF-example of a countable metrizable space whose compact complement topology is not first-countable is given.
- Record ID
- CUT7b5a0986f8994b6b8bb0cb0c6c49b635
- Publication categories
- ;
- Author
- Journal series
- Filomat, ISSN 0354-5180, e-ISSN 2406-0933
- Issue year
- 2019
- Vol
- 33
- No
- 7
- Pages
- 2061-2071
- Other elements of collation
- Bibliografia (na s.) - 2071; Bibliografia (liczba pozycji) - 20; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 33, No 7
- Keywords in English
- compact complement topology, countable multiple choice, k-space, sequential space, Sorgenfrey line, Delfs-Knebusch generalized topological space, partial topology
- DOI
- DOI:10.2298/FIL1907061K Opening in a new tab
- URL
- http://www.pmf.ni.ac.rs/filomat-content/2019/33-7/FILOMAT%2033-7.html Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 40
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT7b5a0986f8994b6b8bb0cb0c6c49b635/
- URN
urn:pkr-prod:CUT7b5a0986f8994b6b8bb0cb0c6c49b635
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.