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Algebra and Discrete Mathematics, 2003, Issue 1, Pages 93–102
(Mi adm372)
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This article is cited in 4 scientific papers (total in 4 papers)
RESEARCH ARTICLE
Uniform ball structures
I. V. Protasov Department Cybernetics, Kyiv
State University, Volodimirska 64, Kyiv 01033, Ukraine
Abstract:
A ball structure is a triple $\mathbb B=(X,P,B)$, where $X,P$ are nonempty sets and, for all $x\in X$, $\alpha \in P$, $B(x,\alpha )$ is a subset of $X, x\in B(x,\alpha)$, which is called a ball of radius $\alpha$ around $x$. We introduce the class of uniform ball structures as an asymptotic counterpart of the class of uniform topological spaces. We show that every uniform ball structure can be approximated by metrizable ball structures. We also define two types of ball structures closed to being metrizable, and describe the extremal elements in the classes of ball structures with fixed support $X$.
Keywords:
ball structure, metrizability.
Received: 31.01.2003
Citation:
I. V. Protasov, “Uniform ball structures”, Algebra Discrete Math., 2003, no. 1, 93–102
Linking options:
https://www.mathnet.ru/eng/adm372 https://www.mathnet.ru/eng/adm/y2003/i1/p93
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