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Theorems · Theorem · several complex variables

CPolynomialAt.eventually_cpolynomialAt

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E},
  CPolynomialAt 𝕜 f x → ∀ᶠ (y : E) in nhds x, CPolynomialAt 𝕜 f y
Defined in
Mathlib.Analysis.Analytic.CPolynomialDef
Cited by
1 results in Mathlib
Foundations
Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CPolynomialAt.exists_mem_nhds_cpolynomialOn · cited by 1CPolynomialAt.exists_mem_…NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldnhds · cited by 5554nhdsFilter.Eventually · cited by 3134Filter.EventuallyIsOpen.mem_nhds · cited by 470IsOpen.mem_nhdsCPolynomialAt · cited by 28CPolynomialAtisOpen_cpolynomialAt · cited by 3isOpen_cpolynomialAtCPolynomialAt.eventually_cpol…CITED BYCITES

Cites8

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Cited by1

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