Manuscript Em02-D@4 · Em02-D-v4.tex · section · fcf2fac7

Exact isolation

Independent separated obstruction and necessary support › Exact isolation · lines 1927–1953

Em02-D@4#eq:isolation

Choose

a = 0, s_{*} = 2 ℓ_{n_{*}}, t_{*} = T_{*} (1, - n_{*}), T_{*} = h /4,

with $z = a - t_{*}$ and $y - a = ℓ_{n_{*}}$ . The point lies where $ζ = 1$ .

On the positive seed, $s = b - a$ and $t = a - z$ are future null, nonzero, and nonparallel. Thus

(b - z)^{2} = (s + t)^{2} > 0, r = - t \neq = 0.

A fixed small neighborhood $O_{A}$ excludes the $47$ and $5 z$ supports, both of which require $b - z$ null, and excludes all response supports, which require $r = 0$ .

Therefore, for every test supported in $O_{A}$ ,

t_{δ}^{ζ} (Φ) = t_{δ, 5 a}^{ζ} (Φ)

at every positive scale. Differentiation does not enlarge internal supports, and only the crossed coefficient is smoothed.

Displayed formulas in this passage

Em02-D@4#eq:isolation · line 1947
$t_{δ}^{ζ} (Φ) = t_{δ, 5 a}^{ζ} (Φ)$
unlabeled · line 1930
$a = 0, s_{*} = 2 ℓ_{n_{*}}, t_{*} = T_{*} (1, - n_{*}), T_{*} = h /4,$
unlabeled · line 1939
$(b - z)^{2} = (s + t)^{2} > 0, r = - t \neq = 0.$