Spaces with large relative extent

Yan-Kui Song

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 387-394
  • ISSN: 0011-4642

Abstract

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In this paper, we prove the following statements: (1) For every regular uncountable cardinal κ , there exist a Tychonoff space X and Y a subspace of X such that Y is both relatively absolute star-Lindelöf and relative property (a) in X and e ( Y , X ) ≥ κ , but Y is not strongly relative star-Lindelöf in X and X is not star-Lindelöf. (2) There exist a Tychonoff space X and a subspace Y of X such that Y is strongly relative star-Lindelöf in X (hence, relative star-Lindelöf), but Y is not absolutely relative star-Lindelöf in X .

How to cite

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Song, Yan-Kui. "Spaces with large relative extent." Czechoslovak Mathematical Journal 57.1 (2007): 387-394. <http://eudml.org/doc/31136>.

@article{Song2007,
abstract = {In this paper, we prove the following statements: (1) For every regular uncountable cardinal $\kappa $, there exist a Tychonoff space $X$ and $Y$ a subspace of $X$ such that $Y$ is both relatively absolute star-Lindelöf and relative property (a) in $X$ and $e(Y,X) \ge \kappa $, but $Y$ is not strongly relative star-Lindelöf in $X$ and $X$ is not star-Lindelöf. (2) There exist a Tychonoff space $X$ and a subspace $Y$ of $X$ such that $Y$ is strongly relative star-Lindelöf in $X$ (hence, relative star-Lindelöf), but $Y$ is not absolutely relative star-Lindelöf in $X$.},
author = {Song, Yan-Kui},
journal = {Czechoslovak Mathematical Journal},
keywords = {relative topological property; Lindelöf; star-Lindelöf; relative extent; relative property (a); relative topological property; Lindelöf; star-Lindelöf; relative extent},
language = {eng},
number = {1},
pages = {387-394},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spaces with large relative extent},
url = {http://eudml.org/doc/31136},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Song, Yan-Kui
TI - Spaces with large relative extent
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 387
EP - 394
AB - In this paper, we prove the following statements: (1) For every regular uncountable cardinal $\kappa $, there exist a Tychonoff space $X$ and $Y$ a subspace of $X$ such that $Y$ is both relatively absolute star-Lindelöf and relative property (a) in $X$ and $e(Y,X) \ge \kappa $, but $Y$ is not strongly relative star-Lindelöf in $X$ and $X$ is not star-Lindelöf. (2) There exist a Tychonoff space $X$ and a subspace $Y$ of $X$ such that $Y$ is strongly relative star-Lindelöf in $X$ (hence, relative star-Lindelöf), but $Y$ is not absolutely relative star-Lindelöf in $X$.
LA - eng
KW - relative topological property; Lindelöf; star-Lindelöf; relative extent; relative property (a); relative topological property; Lindelöf; star-Lindelöf; relative extent
UR - http://eudml.org/doc/31136
ER -

References

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