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