Mapping theorems on countable tightness and a question of F. Siwiec
In this paper -quotient maps and -spaces are introduced. It is shown that (1) countable tightness is characterized by -quotient maps and quotient maps; (2) a space has countable tightness if and only if it is a countably bi-quotient image of a locally countable space, which gives an answer for a question posed by F. Siwiec in 1975; (3) -spaces are characterized as the -quotient images of metric spaces; (4) assuming , a compact -space is an -space if and only if every countably compact subset...