Theorems · Theorem · general topology

ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id

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

Defined in: Mathlib.Topology.ContinuousMap.StoneWeierstrass
Cited by: 1 results in Mathlib
Foundations: Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike

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Cites30

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setstatement and proof · cited by 53,352
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Idealstatement · cited by 4,748
mul_oneproof · cited by 3,885
RCLikestatement and proof · cited by 2,829
add_zeroproof · cited by 2,707
ContinuousMapstatement and proof · cited by 2,491
zero_addproof · cited by 2,366
Set.extproof · cited by 2,266
zero_smulproof · cited by 716

Cited by1

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ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_idproof · cited by 1