Metrizable and weakly metrizable coset spaces

In this paper, we study metrizable and weakly metrizable coset spaces. It is mainly shown that (1) If H is a closed neutral subgroup of a topological group G, then G/H is metrizable double left right arrow G/H is bisequential double left right arrow G/H is weakly first-countable double left right arrow G/H is a Frechet-Urysohn space with an omega(omega)-base; (2) If H is a closed neutral subgroup of a semitopological group G, then G/H is metrizable if and only if G/H is a paracompact feathered space with countable pi-character; (3) If H is a closed neutral subgroup of a paratopological group G such that G/H is a Hausdorff space, then G/H is quasi-metrizable if and only if G/H is first-countable; (4) If H is a closed neutral subgroup of a quasitopological group G, then G/H is semi-metrizable if and only if G/H is first-countable. (c) 2021 Elsevier B.V. All rights reserved.