Geodesic
A quest for nice kernels of neighbourhood assignments
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 4, pp. 689-697.

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

Given a topological property (or a class) $\Cal P$, the class $\Cal P^*$ dual to $\Cal P$ (with respect to neighbourhood assignments) consists of spaces $X$ such that for any neighbourhood assignment $\{O_x:x\in X\}$ there is $Y\subset X$ with $Y\in \Cal P$ and $\bigcup\{O_x:x\in Y\}=X$. The spaces from $\Cal P^*$ are called {\it dually $\Cal P$\/}. We continue the study of this duality which constitutes a development of an idea of E. van Douwen used to define $D$-spaces. We prove a number of results on duals of some general classes of spaces establishing, in particular, that any generalized ordered space of countable extent is dually discrete.
Classification : 22A05, 54C10, 54C25, 54D06, 54D20, 54D25, 54H11
Keywords: neighbourhood assignment; duality; weak duality; Lindelöf space; weakly Lindelöf space 
@article{CMUC_2007__48_4_a11,
     author = {Buzyakova, R. Z. and Tkachuk, V. V. and Wilson, R. G.},
     title = {A quest for nice kernels of neighbourhood assignments},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {689--697},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2007},
     mrnumber = {2375169},
     zbl = {1199.54141},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2007__48_4_a11/}
}
TY  - JOUR
AU  - Buzyakova, R. Z.
AU  - Tkachuk, V. V.
AU  - Wilson, R. G.
TI  - A quest for nice kernels of neighbourhood assignments
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2007
SP  - 689
EP  - 697
VL  - 48
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2007__48_4_a11/
LA  - en
ID  - CMUC_2007__48_4_a11
ER  - 
%0 Journal Article
%A Buzyakova, R. Z.
%A Tkachuk, V. V.
%A Wilson, R. G.
%T A quest for nice kernels of neighbourhood assignments
%J Commentationes Mathematicae Universitatis Carolinae
%D 2007
%P 689-697
%V 48
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2007__48_4_a11/
%G en
%F CMUC_2007__48_4_a11
Buzyakova, R. Z.; Tkachuk, V. V.; Wilson, R. G. A quest for nice kernels of neighbourhood assignments. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 4, pp. 689-697. http://geodesic.mathdoc.fr/item/CMUC_2007__48_4_a11/