Theorems · Definition · functional analysis
ContinuousMapZero.toContinuousMapHom
{X : Type u_1} →
{R : Type u_2} →
[inst : Zero X] →
[inst_1 : TopologicalSpace X] →
[inst_2 : TopologicalSpace R] →
[inst_3 : CommSemiring R] →
[inst_4 : IsTopologicalSemiring R] →
[inst_5 : StarRing R] → [inst_6 : ContinuousStar R] → ContinuousMapZero X R →⋆ₙₐ[R] C(X, R)The coercion C(X, R)₀ → C(X, R) bundled as a non-unital star algebra homomorphism.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- CommSemiringstatement and proof · cited by 10,911
- ContinuousMapstatement · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- ContinuousStarstatement and proof · cited by 543
- IsTopologicalSemiringstatement and proof · cited by 442
- NonUnitalStarAlgHomstatement · cited by 208
- ContinuousMapZerostatement and proof · cited by 167
- toContinuousMapproof · cited by 99
Cited by12
Results whose statement or proof uses this declaration.
- cfcₙ_eq_cfcproof · cited by 13
- cfcₙAuxproof · cited by 11
- cfcₙHom_of_cfcHomproof · cited by 6
- ContinuousMapZero.adjoin_id_denseproof · cited by 3
- RCLike.nonUnitalContinuousFunctionalCalculusproof · cited by 2
- spec_cfcₙAuxproof · cited by 1
- ContinuousMapZero.coe_toContinuousMapHomstatement · cited by 1
- cfcₙHom_of_cfcHom_injectiveproof · cited by 0
- cfcₙHom_of_cfcHom_map_quasispectrumproof · cited by 0
- ContinuousMapZero.toContinuousMapHom_apply_applystatement and proof · cited by 0
- ContinuousMapZero.toContinuousMapHom_toNNRealstatement · cited by 0
- isClosedEmbedding_cfcₙHom_of_cfcHomproof · cited by 0