Spaces with property
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 1, page 131-135
- ISSN: 0010-2628
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topXuan, Wei-Feng, and Shi, Wei-Xue. "Spaces with property $(DC(\omega _1))$." Commentationes Mathematicae Universitatis Carolinae 58.1 (2017): 131-135. <http://eudml.org/doc/287888>.
@article{Xuan2017,
abstract = {We prove that if $X$ is a first countable space with property $(DC(\omega _1))$ and with a $G_\delta $-diagonal then the cardinality of $X$ is at most $\mathfrak \{c\}$. We also show that if $X$ is a first countable, DCCC, normal space then the extent of $X$ is at most $\mathfrak \{c\}$.},
author = {Xuan, Wei-Feng, Shi, Wei-Xue},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$G_\delta $-diagonal; property $(DC(\omega _1))$; cardinal; DCCC},
language = {eng},
number = {1},
pages = {131-135},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Spaces with property $(DC(\omega _1))$},
url = {http://eudml.org/doc/287888},
volume = {58},
year = {2017},
}
TY - JOUR
AU - Xuan, Wei-Feng
AU - Shi, Wei-Xue
TI - Spaces with property $(DC(\omega _1))$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 1
SP - 131
EP - 135
AB - We prove that if $X$ is a first countable space with property $(DC(\omega _1))$ and with a $G_\delta $-diagonal then the cardinality of $X$ is at most $\mathfrak {c}$. We also show that if $X$ is a first countable, DCCC, normal space then the extent of $X$ is at most $\mathfrak {c}$.
LA - eng
KW - $G_\delta $-diagonal; property $(DC(\omega _1))$; cardinal; DCCC
UR - http://eudml.org/doc/287888
ER -
References
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