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 pseudodisc...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2006 |
| ISSN: | 1726-3255 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2006
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/157395 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Pseudodiscrete balleans / O.I. Protasova // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 4. — С. 81–92. — Бібліогр.: 9 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
|
|---|---|
| ISSN: | 1726-3255 |