Submetrizability of strongly topological gyrogroups

Abstract

Topological gyrogroups, with a weaker algebraic structure without associative law, have been investigated recently. We prove that each $T_0$-strongly topological gyrogroup is completely regular. We also prove that every $T_0$-strongly topological gyrogroup with a countable pseudocharacter is submetrizable. Finally, we prove that the left coset space $G/H$ is submetrizable if $H$ is an admissible $L$-subgyrogroup of a $T_0$-strongly topological gyrogroup $G$.

11 pages. arXiv admin note: substantial text overlap with arXiv:1911.12938

References in corpus (1)

• Isomorphism Theorems for Gyrogroups and L-Subgyrogroups

Cited by in corpus (4)

• Strongly Topological Gyrogroups and Quotient With Respect to L-subgyrogroups
• Separability in (strongly) topological gyrogroups
• A class of quotient spaces in strongly topological gyrogroups
• Quotient with respect to admissible $L$-subgyrogroups