Countable Closed Sum Theorems On Wσ-spaces And Strictly Countably Bi-quotient Mappings

In this paper, three kinds of weakly first countable spaces and strictly countably bi-quotientimages of metric spaces are studied. In the first part, strictly Fréchet spaces are characterizedas the spaces in which every sequence-covering mapping onto them is strictly countablybi-quotient; strict accessibility spaces are introduced, in which aT1-space X is strictaccessibility if and only if every quotient mapping onto X is strictly countably bi-quotient;for aT2, k-space X every quotient mapping onto X is strictly countably bi-quotient orbi-quotient if and only if X is discrete, they partially answer the following question posedby F. Siwiec: give an intrinsic characterization of the class of spaces X such that everyquotient mapping onto X is bi-quotient. In the second part, a new characterization and sumtheorems of wσ-spaces are obtained. And we give an affirmative answer to the followingquestion posed by professor S. Lin: Whether wσ-spaces satisfy the countable closed sumtheorems?...