2025/05/22 by Jin, Ying-Ying, Sheng, Ye-Qing, Wang, Yi-Ting +1
#FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2506.00024
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. This means that for every neighborhood U of the identity 0 in G, there exists a countable family γ of neighborhoods of 0 such that for all V ∈γ, \bigcapV∈γ (\ominus V)⊆ U. 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. This means that for every neighborhood U of the identity 0 in G, there exists a countable family γ of neighborhoods of 0 such that for all V ∈γ, \bigcapV∈γ (V\boxminus V)⊆ U.