Theorems · Definition · global analysis
ExistsContDiffBumpBase.u
{E : Type u_1} → [inst : NormedAddCommGroup E] → [inst_1 : NormedSpace ℝ E] → [FiniteDimensional ℝ E] → E → ℝAn auxiliary function to construct partitions of unity on finite-dimensional real vector spaces, which is smooth, symmetric, and with support equal to the unit ball.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 235 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- FiniteDimensionalstatement and proof · cited by 1,854
- ExistsContDiffBumpBase.u_existsproof · cited by 5
Cited by15
Results whose statement or proof uses this declaration.
- ExistsContDiffBumpBase.wproof · cited by 11
- ExistsContDiffBumpBase.u_int_posstatement · cited by 4
- ExistsContDiffBumpBase.u_supportstatement · cited by 4
- ExistsContDiffBumpBase.w_supportproof · cited by 4
- ExistsContDiffBumpBase.u_continuousstatement · cited by 3
- ExistsContDiffBumpBase.u_nonnegstatement · cited by 2
- ExistsContDiffBumpBase.u_smoothstatement · cited by 2
- ExistsContDiffBumpBase.w_defstatement · cited by 2
- ExistsContDiffBumpBase.w_integralproof · cited by 2
- ExistsContDiffBumpBase.u.congr_simpstatement and proof · cited by 1
- ExistsContDiffBumpBase.u_compact_supportstatement · cited by 1
- ExistsContDiffBumpBase.u_negstatement · cited by 1