Abstract
In this paper, we mainly show that the coset space G/H is subsemi-metrizable, whenever H is a closed neutral subgroup of a semitopological group G such that the space G/H is Hausdorff and first-countable. We also prove that if H is a closed subgroup of a quasitopological group G. Then G/H has cardinality at most 2e(G/H)ψ(G/H). These two results answer two questions posed in [22] and [11], respectively.
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