Theorems · Theorem · general topology

ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] (s : Set 𝕜) (h0 : 0 ∈ s) [CompactSpace ↑s],
  ↑(RingHom.ker (ContinuousMap.evalStarAlgHom 𝕜 𝕜 ⟨0, h0⟩)) =
    closure ↑(NonUnitalStarAlgebra.adjoin 𝕜 {ContinuousMap.restrict s (ContinuousMap.id 𝕜)})

Defined in

Mathlib.Topology.ContinuousMap.StoneWeierstrass

Cited by

1 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeCompactSpace