Theorems · Theorem · global analysis
ContinuousMap.dense_setOfPred_contDiff
∀ {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], Dense {f | ContDiff ℝ ↑⊤ ⇑f}Infinitely smooth functions are dense in the space of continuous functions.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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
- Setproof · cited by 53,352
- 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
- Set.ofPredstatement · cited by 6,101
- ENatstatement · cited by 4,985
- CompleteSpacestatement and proof · cited by 2,532
- ContinuousMapstatement and proof · cited by 2,491
- LT.lt.leproof · cited by 2,189
- FiniteDimensionalstatement and proof · cited by 1,854
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.dense_setOf_contDiffproof · cited by 0