, Il s'agit d'un sous-espace fermé G ? -invariant. On peut donner la liste des éléments de K
, On peut maintenant montrer qu'il s'agit d'une description du bord de Furstenberg. L'idée est que l'application gG ? ? C(g?) de G ? /G ? vers K s'étend en un homéomorphisme G ? -équivariant
, Les espaces K et G ? /G ? sont des G-flots isomorphes. En particulier, G ? possède un bord de Furstenberg avec 4 orbites
En effet, tout élément C ? K s'écrit C = C(x) avec x régulier ou x terminal, ce qui donne 2 orbites ou C = C n (b) avec n ? N et b ? Br(D ? ) ce qui donne de nouveaux 2 orbites ,
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