A note on star Lindelöf, first countable and normal spaces

Xuan, Wei-Feng. "A note on star Lindelöf, first countable and normal spaces." Mathematica Bohemica 142.4 (2017): 445-448. <http://eudml.org/doc/294214>.

@article{Xuan2017,
abstract = {A topological space $X$ is said to be star Lindelöf if for any open cover $\mathcal \{U\}$ of $X$ there is a Lindelöf subspace $A \subset X$ such that $\operatorname\{St\}(A, \mathcal \{U\})=X$. The “extent” $e(X)$ of $X$ is the supremum of the cardinalities of closed discrete subsets of $X$. We prove that under $V=L$ every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under $\rm MA +\lnot CH$, which shows that a star Lindelöf, first countable and normal space may not have countable extent.},
author = {Xuan, Wei-Feng},
journal = {Mathematica Bohemica},
keywords = {star Lindelöf space; first countable space; normal space; countable extent},
language = {eng},
number = {4},
pages = {445-448},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on star Lindelöf, first countable and normal spaces},
url = {http://eudml.org/doc/294214},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Xuan, Wei-Feng
TI - A note on star Lindelöf, first countable and normal spaces
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 4
SP - 445
EP - 448
AB - A topological space $X$ is said to be star Lindelöf if for any open cover $\mathcal {U}$ of $X$ there is a Lindelöf subspace $A \subset X$ such that $\operatorname{St}(A, \mathcal {U})=X$. The “extent” $e(X)$ of $X$ is the supremum of the cardinalities of closed discrete subsets of $X$. We prove that under $V=L$ every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under $\rm MA +\lnot CH$, which shows that a star Lindelöf, first countable and normal space may not have countable extent.
LA - eng
KW - star Lindelöf space; first countable space; normal space; countable extent
UR - http://eudml.org/doc/294214
ER -