Binary coronas of balleans

• Published in: Algebra and Discrete Mathematics
• Date: 2003
• Main Author: Protasov, I.V.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2003
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155724
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Binary coronas of balleans / I.V. Protasov // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 50–65. — Бібліогр.: 9 назв. — англ.

A ballean B is a set X endowed with some family
 of subsets of X which are called the balls. We postulate the properties of the family of balls in such a way that a ballean can be
 considered as an asymptotic counterpart of a uniform topological
 space. Using slow oscillating functions from X to {0, 1}, we define
 a zero-dimensional compact space which is called a binary corona
 of B. We define a class of binary normal ballean and, for every ballean from this class, give an intrinsic characterization of its binary
 corona. The class of binary normal balleans contains all balleans
 of graph. We show that a ballean of graph is a projective limit of
 some sequence of C˘ech-Stone compactifications of discrete spaces.
 The obtained results witness that a binary corona of balleans can
 be interpreted as a "generalized space of ends" of ballean.