Theorems · Theorem · algebraic geometry

Function.locallyFinsupp.support_map_subset_of_forall_mem

∀ {X : Type u_1} {Y : Type u_2} {R : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
  (hf : IsSpectralMap f) (w : X → R) [inst_2 : Semiring R] (c : Function.locallyFinsupp X R)
  [inst_3 : PrespectralSpace Y] (s : Set X) (t : Set Y),
  Function.locallyFinsuppWithin.support c ⊆ s →
    (∀ x ∈ s, w x ≠ 0 → f x ∈ t) → Function.locallyFinsuppWithin.support (Function.locallyFinsupp.map f w hf c) ⊆ t

Defined in

Mathlib.Topology.LocallyFinsupp.Pushforward

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceSemiringPrespectralSpace