Theorems · Theorem · general topology

ContinuousMap.mem_idealOfSet

∀ {X : Type u_1} {R : Type u_2} [inst : TopologicalSpace X] [inst_1 : Semiring R] [inst_2 : TopologicalSpace R]
  [inst_3 : IsTopologicalSemiring R] {s : Set X} {f : C(X, R)},
  f ∈ ContinuousMap.idealOfSet R s ↔ ∀ ⦃x : X⦄, x ∈ sᶜ → f x = 0

Defined in

Mathlib.Topology.ContinuousMap.Ideals

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceSemiringTopologicalSpaceIsTopologicalSemiring