Pseudodiscrete balleans
A ballean B is a set X endowed with some family of subsets of X which are called the balls. The properties of the balls are postulated in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. A ballean is called pseudodiscrete if "almost all...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/157395 |
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| Cite this: | Pseudodiscrete balleans / O.I. Protasova // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 4. — С. 81–92. — Бібліогр.: 9 назв. — англ. |
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Protasova, O.I. 2019-06-20T03:12:48Z 2019-06-20T03:12:48Z 2006 Pseudodiscrete balleans / O.I. Protasova // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 4. — С. 81–92. — Бібліогр.: 9 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 03E05, 03E75, 06A11, 54A05, 54E15.. https://nasplib.isofts.kiev.ua/handle/123456789/157395 A ballean B is a set X endowed with some family of subsets of X which are called the balls. The properties of the balls are postulated in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. A ballean is called pseudodiscrete if "almost all" balls of every pregiven radius are singletons. We give a filter characterization of pseudodiscrete balleans and their classification up to quasi-asymorphisms. It is proved that a ballean is pseudodiscrete if and only if every real function defined on its support is slowly oscillating. We show that the class of irresolvable balleans are tightly connected with the class of pseudodiscrete balleans. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Pseudodiscrete balleans Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Pseudodiscrete balleans |
| spellingShingle |
Pseudodiscrete balleans Protasova, O.I. |
| title_short |
Pseudodiscrete balleans |
| title_full |
Pseudodiscrete balleans |
| title_fullStr |
Pseudodiscrete balleans |
| title_full_unstemmed |
Pseudodiscrete balleans |
| title_sort |
pseudodiscrete balleans |
| author |
Protasova, O.I. |
| author_facet |
Protasova, O.I. |
| publishDate |
2006 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
A ballean B is a set X endowed with some family
of subsets of X which are called the balls. The properties of the
balls are postulated in such a way that a ballean can be considered
as an asymptotic counterpart of a uniform topological space. A ballean is called pseudodiscrete if "almost all" balls of every pregiven
radius are singletons. We give a filter characterization of pseudodiscrete balleans and their classification up to quasi-asymorphisms. It
is proved that a ballean is pseudodiscrete if and only if every real
function defined on its support is slowly oscillating. We show that
the class of irresolvable balleans are tightly connected with the class
of pseudodiscrete balleans.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/157395 |
| citation_txt |
Pseudodiscrete balleans / O.I. Protasova // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 4. — С. 81–92. — Бібліогр.: 9 назв. — англ. |
| work_keys_str_mv |
AT protasovaoi pseudodiscreteballeans |
| first_indexed |
2025-12-07T16:08:10Z |
| last_indexed |
2025-12-07T16:08:10Z |
| _version_ |
1850866338873999360 |