This article is cited in 6 papers

RESEARCH ARTICLE

Balleans of bounded geometry and G-spaces

Igor V. Protasov

Kyiv Taras Shevchenko Univ. (for Department of Cybernetics), Volodimirska str., 64, 01033 Kyiv, Ukraine

Abstract: A ballean (or a coarse structure) is a set endowed with some family of subsets which are called the balls. The properties of the family of balls are postulated in such a way that a ballean can be considered as an asymptotical counterpart of a uniform topological space.
We prove that every ballean of bounded geometry is coarsely equivalent to a ballean on some set $X$ determined by some group of permutations of $X$.

Keywords: ballean, coarse equivalence, G-space.

MSC: 37B05, 54E15

Received: 23.03.2008
Revised: 23.03.2008

Language: English

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