Theorems · Theorem · global analysis
UniformContinuous.exists_contDiff_dist_le
∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E]
[inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] [CompleteSpace F] {f : E → F} {ε : ℝ},
UniformContinuous f → 0 < ε → ∃ g, ContDiff ℝ (↑⊤) g ∧ ∀ (a : E), dist (g a) (f a) < ε- Cited by
- 0 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topstatement and proof · cited by 9,680
- ENatstatement · cited by 4,985
- CompleteSpacestatement and proof · cited by 2,532
- LT.lt.leproof · cited by 2,189
- FiniteDimensionalstatement and proof · cited by 1,854
- Dist.diststatement and proof · cited by 1,539
- WithTop.somestatement and proof · cited by 1,128
- LE.le.trans_ltproof · cited by 795
- Metric.ballproof · cited by 735
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