Definition: Functional support and ordering

A point belongs to ${\mathrm{supp}}_{\mathrm{fun}}F$ if every neighbourhood admits a compactly supported smooth perturbation that changes $F$ at some smooth configuration. For formal polynomials, support means the union of the supports of their finitely many coefficients. Species supports ${\mathrm{supp}}_{h}F,{\mathrm{supp}}_{\varphi }F$ use only the corresponding variations.

Define