Spaces with countable s n -networks

Ge Ying

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 1, page 169-176
  • ISSN: 0010-2628

Abstract

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In this paper, we prove that a space X is a sequentially-quotient π -image of a metric space if and only if X has a point-star s n -network consisting of c s * -covers. By this result, we prove that a space X is a sequentially-quotient π -image of a separable metric space if and only if X has a countable s n -network, if and only if X is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable s n -networks.

How to cite

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Ying, Ge. "Spaces with countable $sn$-networks." Commentationes Mathematicae Universitatis Carolinae 45.1 (2004): 169-176. <http://eudml.org/doc/249333>.

@article{Ying2004,
abstract = {In this paper, we prove that a space $X$ is a sequentially-quotient $\pi $-image of a metric space if and only if $X$ has a point-star $sn$-network consisting of $cs^*$-covers. By this result, we prove that a space $X$ is a sequentially-quotient $\pi $-image of a separable metric space if and only if $X$ has a countable $sn$-network, if and only if $X$ is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable $sn$-networks.},
author = {Ying, Ge},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {separable metric space; sequentially-quotient ($\pi $; compact) mapping; point-star $sn$-network; $cs*$-cover; separable metric space; sequentially-quotient (, compact) mapping; point-star -network; -cover},
language = {eng},
number = {1},
pages = {169-176},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Spaces with countable $sn$-networks},
url = {http://eudml.org/doc/249333},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Ying, Ge
TI - Spaces with countable $sn$-networks
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 1
SP - 169
EP - 176
AB - In this paper, we prove that a space $X$ is a sequentially-quotient $\pi $-image of a metric space if and only if $X$ has a point-star $sn$-network consisting of $cs^*$-covers. By this result, we prove that a space $X$ is a sequentially-quotient $\pi $-image of a separable metric space if and only if $X$ has a countable $sn$-network, if and only if $X$ is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable $sn$-networks.
LA - eng
KW - separable metric space; sequentially-quotient ($\pi $; compact) mapping; point-star $sn$-network; $cs*$-cover; separable metric space; sequentially-quotient (, compact) mapping; point-star -network; -cover
UR - http://eudml.org/doc/249333
ER -

References

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