Abstract
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 ⇔ G/H is bisequential ⇔ G/H is weakly first-countable ⇔ G/H is a Fréchet-Urysohn space with an ωω-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 π-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.
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