g -metrizable spaces and the images of semi-metric spaces

Ying Ge; Shou Lin

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 4, page 1141-1149
  • ISSN: 0011-4642

Abstract

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In this paper, we prove that a space X is a g -metrizable space if and only if X is a weak-open, π and σ -image of a semi-metric space, if and only if X is a strong sequence-covering, quotient, π and m s s c -image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.

How to cite

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Ge, Ying, and Lin, Shou. "$g$-metrizable spaces and the images of semi-metric spaces." Czechoslovak Mathematical Journal 57.4 (2007): 1141-1149. <http://eudml.org/doc/31186>.

@article{Ge2007,
abstract = {In this paper, we prove that a space $X$ is a $g$-metrizable space if and only if $X$ is a weak-open, $\pi $ and $\sigma $-image of a semi-metric space, if and only if $X$ is a strong sequence-covering, quotient, $\pi $ and $mssc$-image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.},
author = {Ge, Ying, Lin, Shou},
journal = {Czechoslovak Mathematical Journal},
keywords = {$g$-metrizable spaces; $sn$-metrizable spaces; weak-open mappings; strong sequence-covering mappings; quotient mappings; $\pi $-mappings; $\sigma $-mappings; $mssc$-mappings; -metrizable spaces; weak-open mappings},
language = {eng},
number = {4},
pages = {1141-1149},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$g$-metrizable spaces and the images of semi-metric spaces},
url = {http://eudml.org/doc/31186},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Ge, Ying
AU - Lin, Shou
TI - $g$-metrizable spaces and the images of semi-metric spaces
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 1141
EP - 1149
AB - In this paper, we prove that a space $X$ is a $g$-metrizable space if and only if $X$ is a weak-open, $\pi $ and $\sigma $-image of a semi-metric space, if and only if $X$ is a strong sequence-covering, quotient, $\pi $ and $mssc$-image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.
LA - eng
KW - $g$-metrizable spaces; $sn$-metrizable spaces; weak-open mappings; strong sequence-covering mappings; quotient mappings; $\pi $-mappings; $\sigma $-mappings; $mssc$-mappings; -metrizable spaces; weak-open mappings
UR - http://eudml.org/doc/31186
ER -

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