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

Shou Lin; Jinhuang Zhang

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 4, page 523-536
  • ISSN: 0010-2628

Abstract

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In this paper s s -quotient maps and s s q -spaces are introduced. It is shown that (1) countable tightness is characterized by s s -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) s s q -spaces are characterized as the s s -quotient images of metric spaces; (4) assuming 2 ω < 2 ω 1 , a compact T 2 -space is an s s q -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.

How to cite

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Lin, Shou, and Zhang, Jinhuang. "Mapping theorems on countable tightness and a question of F. Siwiec." Commentationes Mathematicae Universitatis Carolinae 55.4 (2014): 523-536. <http://eudml.org/doc/262044>.

@article{Lin2014,
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.},
author = {Lin, Shou, Zhang, Jinhuang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
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},
language = {eng},
number = {4},
pages = {523-536},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Mapping theorems on countable tightness and a question of F. Siwiec},
url = {http://eudml.org/doc/262044},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Lin, Shou
AU - Zhang, Jinhuang
TI - Mapping theorems on countable tightness and a question of F. Siwiec
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 4
SP - 523
EP - 536
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/262044
ER -

References

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