Parties bornées d'un espace topologique complètement régulier
Partition continue de l'unite et C-repletion.
Pointwise convergence fails to be strict
It is known that the ring of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of which differs from .
Primarité des espaces ( ordinal infini premier ordinal non dénombrable)
Prolongement dans des classes ultradifférentiables et propriétés de régularité des compacts de
Considering jets, or functions, belonging to some strongly non-quasianalytic Carleman class on compact subsets of , we extend them to the whole space with a loss of Carleman regularity. This loss is related to geometric conditions refining Łojasiewicz’s “regular separation” or Whitney’s “property (P)”.