Mapping theorems on countable tightness and a question of F. Siwiec

Lin, Shou ; Zhang, Jinhuang

Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 4, pp. 523-536.

Résumé

In this paper $ss$-quotient maps and $ssq$-spaces are introduced. It is shown that (1) countable tightness is characterized by $ss$-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) $ssq$-spaces are characterized as the $ss$-quotient images of metric spaces; (4) assuming $2^\omega2^{\omega_1}$, a compact $T_2$-space is an $ssq$-space if and only if every countably compact subset is strongly sequentially closed, which improves some results about sequential spaces obtained by M. Ismail and P. Nyikos in 1980.

Détail

Classification : 54B15, 54D55, 54E40
Keywords: countable tightness; strongly sequentially closed sets; sequentially closed sets; quotient maps; countably bi-quotient maps; locally countable spaces