Generalized metrizable properties and cardinal invariants in quotient spaces of quasitopological groups

Abstract

In this paper, we study some generalized metrizable properties and cardinal invariants in quotient spaces of quasitopological groups. We mainly show that (1) If H is a neutral subgroup of a quasitopological group G such that G/H is Hausdorff, then G/H is weakly first-countable if and only if G/H is symmetrizable; (2) If H is a neutral subgroup of a quasitopological group G such that G/H is a Hausdorff countably compact space of countable pseudocharacter, then G/H is metrizable; (3) If H is a neutral subgroup of a quasitopological group G such that G/H is a q-space, then G/H is a β-space; (4) If H is a closed neutral subgroup of a quasitopological group G, then |G/H|≤2e(G/H)ψ(G/H).