Geodesic
Remarks on discretely absolutely star-Lindelöf spaces
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 823-831 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we prove the following statements: \item {(1)} There exists a Hausdorff Lindelöf space $X$ such that the Alexandroff duplicate $A(X)$ of $X$ is not discretely absolutely star-Lindelöf. \item {(2)} If $X$ is a regular Lindelöf space, then $A(X)$ is discretely absolutely star-Lindelöf. \item {(3)} If $X$ is a normal discretely star-Lindelöf space with $e(X) \omega _1$, then $A(X)$ is discretely absolutely star-Lindelöf.
In this paper, we prove the following statements: \item {(1)} There exists a Hausdorff Lindelöf space $X$ such that the Alexandroff duplicate $A(X)$ of $X$ is not discretely absolutely star-Lindelöf. \item {(2)} If $X$ is a regular Lindelöf space, then $A(X)$ is discretely absolutely star-Lindelöf. \item {(3)} If $X$ is a normal discretely star-Lindelöf space with $e(X) \omega _1$, then $A(X)$ is discretely absolutely star-Lindelöf.
Classification : 54B10, 54D20, 54D55
Keywords: countably compact space; star-Lindelöf space; absolutely star-Lindelöf space; discretely absolutely star-Lindelöf 
@article{CMJ_2008_58_3_a16,
     author = {Song, Yan-Kui},
     title = {Remarks on discretely absolutely {star-Lindel\"of} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {823--831},
     year = {2008},
     volume = {58},
     number = {3},
     mrnumber = {2455940},
     zbl = {1174.54015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a16/}
}
TY  - JOUR
AU  - Song, Yan-Kui
TI  - Remarks on discretely absolutely star-Lindelöf spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2008
SP  - 823
EP  - 831
VL  - 58
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a16/
LA  - en
ID  - CMJ_2008_58_3_a16
ER  - 
%0 Journal Article
%A Song, Yan-Kui
%T Remarks on discretely absolutely star-Lindelöf spaces
%J Czechoslovak Mathematical Journal
%D 2008
%P 823-831
%V 58
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a16/
%G en
%F CMJ_2008_58_3_a16
Song, Yan-Kui. Remarks on discretely absolutely star-Lindelöf spaces. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 823-831. http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a16/