Quotient spaces of strongly topological gyrogroups

Abstract

The concept of gyrogroups was introduced during the researches of Einstein velocity addition that Einstein introduced in [15] which founded the special theory of relativity. In this paper, we mainly investigate the quotient spaces generated from a strongly topological gyrogroup with respect to closed strong subgyrogroups. It is shown that if G is a strongly topological gyrogroup and H is a closed first-countable and separable strong subgyrogroup of G, the quotient space G/H is an ℵ0-space, then G is an ℵ0-space; if the quotientspace G/H is a cosmic space, then G is also a cosmic space; if the quotient space G/H has a star-countable cs-network or star-countable wcs∗-network, then G also has a star-countable cs-network or star-countable wcs∗-network, respectively

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