Geodesic
On some classes of spaces with the $D$-property
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 2, pp. 247-256.

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

We shall prove that under CH every regular meta-Lindelöf $P$-space which is locally $D$ has the $D$-property. In addition, we shall prove that a regular submeta-Lindelöf $P$-space is $D$ if it is locally $D$ and has locally extent at most $\omega_1$. Moreover, these results can be extended from the class of locally $D$-spaces to the wider class of $\mathbb D$-scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology Appl. 157 (2010), 378--384] which states that every weak $\overline{\theta}$-refinable $\mathbb D$-scattered space is $D$.
Classification : 54A35, 54D20, 54G10
Keywords: property $D$; meta-Lindelöf; weak $\overline{\theta}$-refinable; $P$-space; scattered space 
@article{CMUC_2014__55_2_a9,
     author = {Mart{\'\i}nez, Juan Carlos},
     title = {On some classes of spaces with the $D$-property},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {247--256},
     publisher = {mathdoc},
     volume = {55},
     number = {2},
     year = {2014},
     mrnumber = {3193929},
     zbl = {06391541},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2014__55_2_a9/}
}
TY  - JOUR
AU  - Martínez, Juan Carlos
TI  - On some classes of spaces with the $D$-property
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2014
SP  - 247
EP  - 256
VL  - 55
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2014__55_2_a9/
LA  - en
ID  - CMUC_2014__55_2_a9
ER  - 
%0 Journal Article
%A Martínez, Juan Carlos
%T On some classes of spaces with the $D$-property
%J Commentationes Mathematicae Universitatis Carolinae
%D 2014
%P 247-256
%V 55
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2014__55_2_a9/
%G en
%F CMUC_2014__55_2_a9
Martínez, Juan Carlos. On some classes of spaces with the $D$-property. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 2, pp. 247-256. http://geodesic.mathdoc.fr/item/CMUC_2014__55_2_a9/