Theorems · Definition · ordinary differential equations
ODE.FunSpace.toContinuousMap
{E : Type u_1} →
[inst : NormedAddCommGroup E] →
{tmin tmax : ℝ} →
{t₀ : ↑(Set.Icc tmin tmax)} → {x₀ : E} → {r L : NNReal} → ODE.FunSpace t₀ x₀ r L ↪ C(↑(Set.Icc tmin tmax), E)The embedding of FunSpace into the space of continuous maps
- Defined in
- Mathlib.Analysis.ODE.PicardLindelof
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Set.Elemstatement and proof · cited by 7,166
- NNRealstatement and proof · cited by 4,310
- ContinuousMapstatement · cited by 2,491
- Set.Iccstatement and proof · cited by 1,702
- Function.Embeddingstatement · cited by 988
- ODE.FunSpacestatement and proof · cited by 37
- ODE.FunSpace.toFunproof · cited by 20
- ODE.FunSpace.continuousproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- ODE.FunSpace.dist_iterate_next_iterate_next_leproof · cited by 2
- ODE.FunSpace.toContinuousMap_apply_eq_applystatement · cited by 1
- ODE.FunSpace.dist_next_nextproof · cited by 1
- ODE.FunSpace.isUniformInducing_toContinuousMapstatement · cited by 0
- ODE.FunSpace.range_toContinuousMapstatement and proof · cited by 0