Geodesic
Addition theorems, $D$-spaces and dually discrete spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 1, pp. 113-124.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A {\it neighbourhood assignment\/} in a space $X$ is a family $\Cal O= \{O_x:x\in X\}$ of open subsets of $X$ such that $x\in O_x$ for any $x\in X$. A set $Y\subseteq X$ is {\it a kernel of $\Cal O$\/} if $\Cal O(Y)=\bigcup\{O_x:x\in Y\}=X$. If every neighbourhood assignment in $X$ has a closed and discrete (respectively, discrete) kernel, then $X$ is said to be a $D$-space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf $P$-space is a $D$-space and we prove an addition theorem for metalindelöf spaces which answers a question of Arhangel'skii and Buzyakova.
Classification : 54D20, 54G99
Keywords: neighbourhood assignment; $D$-space; dually discrete space; discrete kernel; scattered space; paracompactness; GO-space 
@article{CMUC_2009__50_1_a9,
     author = {Alas, Ofelia T. and Tkachuk, Vladimir V. and Wilson, Richard G.},
     title = {Addition theorems, $D$-spaces and dually discrete spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {113--124},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {2009},
     mrnumber = {2562808},
     zbl = {1212.54074},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2009__50_1_a9/}
}
TY  - JOUR
AU  - Alas, Ofelia T.
AU  - Tkachuk, Vladimir V.
AU  - Wilson, Richard G.
TI  - Addition theorems, $D$-spaces and dually discrete spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2009
SP  - 113
EP  - 124
VL  - 50
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2009__50_1_a9/
LA  - en
ID  - CMUC_2009__50_1_a9
ER  - 
%0 Journal Article
%A Alas, Ofelia T.
%A Tkachuk, Vladimir V.
%A Wilson, Richard G.
%T Addition theorems, $D$-spaces and dually discrete spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 2009
%P 113-124
%V 50
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2009__50_1_a9/
%G en
%F CMUC_2009__50_1_a9
Alas, Ofelia T.; Tkachuk, Vladimir V.; Wilson, Richard G. Addition theorems, $D$-spaces and dually discrete spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 1, pp. 113-124. http://geodesic.mathdoc.fr/item/CMUC_2009__50_1_a9/