Theorems · Theorem · functional analysis
ContDiffMapSupportedIn.norm_toBoundedContinuousFunction
∀ (𝕜 : Type u_1) {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace ℝ E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace 𝕜 F]
[inst_6 : SMulCommClass ℝ 𝕜 F] {n : ℕ∞} {K : TopologicalSpace.Compacts E} (f : ContDiffMapSupportedIn E F n K),
‖{ toFun := ⇑f, continuous_toFun := ⋯, map_bounded' := ⋯ }‖ = (ContDiffMapSupportedIn.seminorm 𝕜 E F n K 0) f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- ENatstatement and proof · cited by 4,985
- iSupproof · cited by 2,415
- SMulCommClassstatement and proof · cited by 1,927
- BoundedContinuousFunctionstatement · cited by 511
- TopologicalSpace.Compactsstatement and proof · cited by 386
- CharP.cast_eq_zeroproof · cited by 357
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