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Balleans, hyperballeans and ideals

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Balleans, hyperballeans and ideals

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Dikranjan, D.; Protasov, I.; Protasova, K.; Zava, N. (2019). Balleans, hyperballeans and ideals. Applied General Topology. 20(2):431-447. https://doi.org/10.4995/agt.2019.11645

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Título: Balleans, hyperballeans and ideals
Autor: Dikranjan, Dikran Protasov, Igor Protasova, Ksenia Zava, Nicolò
Fecha difusión:
Resumen:
[EN] A ballean B (or a coarse structure) on a set X is a family of subsets of X called balls (or entourages of the diagonal in X × X) dened in such a way that B can be considered as the asymptotic counterpart of a uniform ...[+]
Palabras clave: Balleans , Coarse structure , Coarse map , Asymorphism , Balleans defined by ideals , Hyperballeans
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2019.11645
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2019.11645
Agradecimientos:
The first named author thankfully acknowledges partial financial support via the grant PRID at the Department of Mathematical,Computer and Physical Sciences, Udine University.
Tipo: Artículo

References

T. Banakh, I. Protasov, D. Repovs and S. Slobodianiuk, Classifying homogeneous cellular ordinal balleans up to coarse equivalence, arxiv: 1409.3910v2.

T. Banakh and I. Zarichnyi, Characterizing the Cantor bi-cube in asymptotic categories, Groups, Geometry and Dynamics 5 (2011), 691-728. https://doi.org/10.4171/GGD/145

W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Grundlehren der mathematischen Wissenschaften, Band 211, Springer--Verlag, Berlin-Heidelberg-New York, 1974. [+]
T. Banakh, I. Protasov, D. Repovs and S. Slobodianiuk, Classifying homogeneous cellular ordinal balleans up to coarse equivalence, arxiv: 1409.3910v2.

T. Banakh and I. Zarichnyi, Characterizing the Cantor bi-cube in asymptotic categories, Groups, Geometry and Dynamics 5 (2011), 691-728. https://doi.org/10.4171/GGD/145

W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Grundlehren der mathematischen Wissenschaften, Band 211, Springer--Verlag, Berlin-Heidelberg-New York, 1974.

D. Dikranjan and N. Zava, Some categorical aspects of coarse structures and balleans, Topology Appl. 225 (2017), 164--194. https://doi.org/10.1016/j.topol.2017.04.011

D. Dikranjan and N. Zava, Preservation and reflection of size properties of balleans, Topology Appl. 221 (2017), 570--595. https://doi.org/10.1016/j.topol.2017.02.008

A. Dow, Closures of discrete sets in compact spaces, Studia Sci. Math. Hungar. 42, no. 2 (2005), 227--234. https://doi.org/10.1556/SScMath.42.2005.2.7

K. Kunen, Set theory. An introduction to independence proofs, Studies in Logic and Foundations of Math., vol. 102, North-Holland, Amsterdam-New York-Oxford, 1980.

O. Petrenko and I. Protasov, Balleans and filters, Mat. Stud. 38, no. 1 (2012), 3--11. https://doi.org/10.1007/s11253-012-0653-x

I. Protasov and T. Banakh, Ball Structures and Colorings of Groups and Graphs, Mat. Stud. Monogr. Ser 11, VNTL, Lviv, 2003.

I. Protasov and K. Protasova, On hyperballeans of bounded geometry, arXiv:1702.07941v1.

I. Protasov and M. Zarichnyi, General Asymptology, 2007 VNTL Publishers, Lviv, Ukraine.

J. Roe, Lectures on Coarse Geometry, Univ. Lecture Ser., vol. 31, American Mathematical Society, Providence RI, 2003. https://doi.org/10.1090/ulect/031

N. Zava, On F-hyperballeans, work in progress.

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