Theorems · Theorem · general topology

ContinuousMap.notMem_setOfIdeal

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

Defined in

Mathlib.Topology.ContinuousMap.Ideals

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceSemiringTopologicalSpaceIsTopologicalSemiring