Abstract Almost s s -mappings and almost compact mappings have been introduced studied. In this article, we continue to research some questions related the -images (resp., images) of metric spaces. The following results are obtained. (1) A space X X is a quotient image if only sequential having c</m:...

In this paper it is studied the role of the axiom of choice in some theorems in which the concepts of first and second countability are used. Results such as the following are established: (1) In ZF (Zermelo–Fraenkel set theory without the axiom of choice), equivalent are: (i) every base of a second countable space has a countable subfamily which is a base; (ii) the axiom of countable choice fo...