Manuscript X-F-ST@1 · X-F-ST.tex · section · e71f03ef

The scalar fixed-support sheet

Topology, support transport, and diagnostic checks › The scalar fixed-support sheet · lines 1945–1960

For compact $A \subset M$ , define

D_{A} = {a \in C_{c}^{\infty} (M; C) : supp a \subset A}, p_{N} (a) = ∣ α ∣ \leq N max sup ∣ \partial^{α} a ∣.

These are ambient fixed-support smooth spaces, not spaces of functions defined only on the compact set.

The scalar degree-one quotient is

Q_{m} = D / P_{m} D, D = C_{c}^{\infty} (M; C) .

Displayed formulas in this passage

unlabeled · line 1948
$D_{A} = {a \in C_{c}^{\infty} (M; C) : supp a \subset A}, p_{N} (a) = ∣ α ∣ \leq N max sup ∣ \partial^{α} a ∣.$
unlabeled · line 1957
$Q_{m} = D / P_{m} D, D = C_{c}^{\infty} (M; C) .$