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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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