A note on countably bi-quotient mappings

摘要

In this paper some properties of weakly first countable spaces and sequencecovering images of metric spaces are studied. Strictly Fréchet spaces are characterized as the spaces in which every sequence-covering mapping onto them is strictly countably bi-quotient. Strict accessibility spaces are introduced, in which a T _1-space X is strict accessibility if and only if every quotient mapping onto X is strictly countably biquotient. For a T _2, k-space X every quotient mapping onto X is strictly countably bi-quotient or bi-quotient if and only if X is discrete. They partially answer some questions posed by F. Siwiec in [16, 17].