Partially paratopological groups
Authors:
- Cenap Özel,
- Artur Piękosz,
- Mohammed Al Shumrani,
- Eliza Wajch
Abstract
In this paper, we introduce the notion of a partially (para)topological group, using generalized topology in the sense of H. Delfs and M. Knebusch. We study some basic properties of this kind of structures. Among them, we prove that an important theorem of Banakh and Ravsky, applied to their proof in ZFC that every regular paratopological group is completely regular, can be false in a model for ZF. Therefore, it is an open problem whether there exists a model for ZF in which a Hausdorff topological group need not be completely regular. We notice that Banakh–Ravsky theorem that every regular paratopological group is completely regular is provable in every model for ZF+DCZF+DC.
- Record ID
- CUTd17c272bfc8d4c8885d2f046b0e210ef
- Publication categories
- ;
- Author
- Journal series
- Topology and its Applications, ISSN 0166-8641, e-ISSN 1879-3207
- Issue year
- 2017
- Vol
- 228
- Pages
- 68-78
- Other elements of collation
- Bibliografia (na s.) - 78; Bibliografia (liczba pozycji) - 15; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 228
- Keywords in English
- generalized topology, strict continuity, partially topological group, partially paratopological group
- DOI
- DOI:10.1016/j.topol.2017.05.006 Opening in a new tab
- URL
- http://www.sciencedirect.com/science/article/pii/S0166864117302742 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTd17c272bfc8d4c8885d2f046b0e210ef/
- URN
urn:pkr-prod:CUTd17c272bfc8d4c8885d2f046b0e210ef
* 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.