A note on countably bi-quotient mappings

Abstract

In this paper some properties of weakly first countable spaces and sequence-covering 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 T₁-space X is strict accessibility if and only if every quotient mapping onto X is strictly countably bi-quotient. For a T₂, 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].