Thin subsets of balleans

Lutsenko, Ievgen ^[1] ; Protasov, Igor V. ^[1]
1. [1] Kyiv University
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 11, Nº. 2, 2010, págs. 89-93
Idioma: inglés
DOI: 10.4995/agt.2010.1710
Enlaces
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Resumen
- A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpar tof a uniform topological space. We characterize the ideal generated by the family of all thin subsets in an ordinal ballean, and apply this characterization to metric spaces and groups.
Referencias bibliográficas
- A. Bella and V. Malykhin, On certain subsets of groups, Questions Answers Gen. Topology 17 (1999), 183–187.
- M. Filali and I. V. Protasov, Spread of balleans, Appl. Gen. Topol. 9 (2008), 169–175.
- F. Harary, Graph Theory, Addison-Wesley Publ. Comp., 1969.
- Ie. Lutsenko and I. V. Protasov, Sparse, thin and other subsets of groups, Internat. J. of Algebra Comput. 19 (2009), 491–510. http://dx.doi.org/10.1142/S0218196709005135
- I. Protasov and M. Zarichnyi, General Asymptology, Math. Stud. Monogr. Ser., Vol. 11, VNTL Publishers, Lviv, 2007.
- O. Protasova, Pseudodiscrete balleans, Algebra Discrete Math. 4 (2006), 81–92.
- J. Roe, Lecture on Coarse Geometry, AMS University Lecture Ser. 31 (2003).