Manuscript XV-E@1 · XV-E.tex · definition · a3dc45f5

Definition

Descending extensions in the punctured normal-jet module › Annihilator ideals · lines 608–613

$Ann (T^{\circ}) = {g \in C^{\infty} (X) : g ∣_{X^{\circ}} T^{\circ} = 0}$ and, for $T \in D^{'} (X)$ , $Ann (T) = {g \in C^{\infty} (X) : g T = 0}$ . Both are ideals of $C^{\infty} (X)$ , and $Ann (T) \subseteq Ann (T^{\circ})$ when $T$ extends $T^{\circ}$ .

Nearby in this section

lemma: Lemma: β is surjective
theorem: Theorem: Annihilator criterion for the null defect