Subgyrogroups within the product spaces of paratopological gyrogroups
Abstract
We present a characterization of paratopological gyrogroups that can be topologically embedded as subgyrogroups into a product of first-countable Ti paratopological gyrogroups for i = 0, 1, 2. Specifically, we demonstrate that a strongly paratopological gyrogroup G is topologically isomorphic to a subgyrogroup of a topological product of first-countable T1 strongly paratopological gyrogroups if and only if G is T1, ω-balanced and the weakly Hausdorff number of G is countable. Similarly, we prove that a strongly paratopological gyrogroup G is topologically isomorphic to a subgyrogroup of a topological product of first-countable Hausdorff strongly paratopological gyrogroups if and only if G is Hausdorff, ω-balanced and the Hausdorff number of G is countable.
Fields of Study & Subjects
Mathematics and Applications
Historical Geography and Cartography
Publication details
- Journal / source
- Quaestiones Mathematicae
- Publisher
- National Inquiry Services Center (NISC)
- Volume
- 49
- Issue
- 10
- Pages
- 1371–1394
- Publication date
- 5 May 2026
- Language
- EN