TY - JOUR
AU - Protasov, Igor V.
PY - 2019/04/01
Y2 - 2022/12/01
TI - Extremal balleans
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 20
IS - 1
SE -
DO - 10.4995/agt.2019.11260
UR - https://polipapers.upv.es/index.php/AGT/article/view/11260
SP - 297-305
AB - <p>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 ultra-normal (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'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.</p>
ER -