## Shou Lin, Jinhuang Zhang

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

Comment.Math.Univ.Carolin. 55,4 (2014) 523-536.**Abstract:**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 $2^\omega<2^{\omega_1}$, 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.

**Keywords:** countable tightness; strongly sequentially closed sets; sequentially closed sets; quotient maps; countably bi-quotient maps; locally countable spaces

**AMS Subject Classification:** 54B15 54D55 54E40

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