Manuscript IX-Free-2@1 · IX-Free-2.tex · section · abb2397a

Gate T: fixed-support continuity and its boundary

Gate T: fixed-support continuity and its boundary · lines 1633–1647

Fix compact sets

K_{1}, K_{2}, K_{3} ⋐ M_{+}, D_{K_{i}} = {f \in C_{c}^{\infty} (M_{+}) : supp f \subset K_{i}} .

These are Fréchet spaces with their usual smooth seminorms.

We first record the continuity argument needed for classical products of inherited families.

Displayed formulas in this passage

unlabeled · line 1637
$K_{1}, K_{2}, K_{3} ⋐ M_{+}, D_{K_{i}} = {f \in C_{c}^{\infty} (M_{+}) : supp f \subset K_{i}} .$