Geodesic
Open ultrafilters and separability with the use of the operation of closure
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 212-225

Voir la notice de l'article provenant de la source Math-Net.Ru

We study ultrafilters of topologies as well as sets of ultrafilters that each time dominate the open neighborhood filter of some fixed point in a topological space. The sets of ultrafilters are considered as “enlarged points” of the original space. We study conditions that provide the discernibility of (enlarged) “points” of this type. We use nontraditional separability axioms and study their connection with the known axioms $T_0$, $T_1$, and $T_2.$
Keywords: closure, neighborhood, ultrafilter. 
@article{TIMM_2016_22_3_a21,
     author = {E. G. Pytkeev and A. G. Chentsov},
     title = {Open ultrafilters and separability with the use of the operation of closure},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {212--225},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a21/}
}
TY  - JOUR
AU  - E. G. Pytkeev
AU  - A. G. Chentsov
TI  - Open ultrafilters and separability with the use of the operation of closure
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2016
SP  - 212
EP  - 225
VL  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a21/
LA  - ru
ID  - TIMM_2016_22_3_a21
ER  - 
%0 Journal Article
%A E. G. Pytkeev
%A A. G. Chentsov
%T Open ultrafilters and separability with the use of the operation of closure
%J Trudy Instituta matematiki i mehaniki
%D 2016
%P 212-225
%V 22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a21/
%G ru
%F TIMM_2016_22_3_a21
E. G. Pytkeev; A. G. Chentsov. Open ultrafilters and separability with the use of the operation of closure. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 212-225. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a21/