Theorems · Theorem · general topology

ContinuousMap.adjoin_id_eq_span_one_union

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] (s : Set 𝕜),
  ↑(StarAlgebra.adjoin 𝕜 {ContinuousMap.restrict s (ContinuousMap.id 𝕜)}) =
    ↑(Submodule.span 𝕜 ({1} ∪ ↑(NonUnitalStarAlgebra.adjoin 𝕜 {ContinuousMap.restrict s (ContinuousMap.id 𝕜)})))

Defined in: Mathlib.Topology.ContinuousMap.StoneWeierstrass
Cited by: 0 results in Mathlib
Foundations: Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike

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

Setstatement and proof · cited by 53,352
SetLike.coestatement and proof · cited by 8,199
Submodulestatement and proof · cited by 7,192
Set.Elemstatement and proof · cited by 7,166
RCLikestatement and proof · cited by 2,829
ContinuousMapstatement and proof · cited by 2,491
Set.extproof · cited by 2,266
Submodule.spanstatement and proof · cited by 1,504
SetLike.mem_coeproof · cited by 302
NonUnitalStarSubalgebrastatement · cited by 196
StarSubalgebrastatement and proof · cited by 194
ContinuousMap.idstatement and proof · cited by 73

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