Extremal balleans

• Autores: Igor V. Protasov
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 1, 2019, págs. 297-305
• Idioma: inglés
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• Resumen

  • A ballean (or coarse space) is a set endowed with a coarse structure.A ballean $X$ is called normal if any two asymptotically disjoint subsets of $X$ are asymptotically separated.We say that a ballean $X$ is ultranormal (extremely normal) if any two unbounded subsets of $X$ are not asymptotically disjoint (every unbounded subset of $X$ is large).Every maximal ballean is extremely normal and every extremely normal ballean is ultranormal, but the converse statements do not hold.A normal ballean is ultranormal if and only if the Higson$^{\prime}$s corona of $X$ is a singleton.A discrete ballean $X$ is ultranormal if and only if $X$ is maximal.We construct a series of concrete balleans with extremal properties.