Theorems · Theorem · global analysis
IsOpen.uniqueDiffWithinAt
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : DivisionSemiring 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [inst_4 : TopologicalSpace 𝕜] [(nhdsWithin 0 {0}ᶜ).NeBot] [ContinuousSMul 𝕜 E] {x : E}
{s : Set E} [ContinuousAdd E], IsOpen s → x ∈ s → UniqueDiffWithinAt 𝕜 s x- Cited by
- 7 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Compl.complstatement and proof · cited by 2,925
- IsOpenstatement and proof · cited by 2,400
- nhdsWithinstatement and proof · cited by 1,912
- ContinuousSMulstatement and proof · cited by 1,016
- Filter.NeBotstatement and proof · cited by 853
- ContinuousAddstatement and proof · cited by 777
- IsOpen.mem_nhdsproof · cited by 470
- UniqueDiffWithinAtstatement · cited by 252
Cited by7
Results whose statement or proof uses this declaration.
- IsOpen.uniqueDiffOnproof · cited by 15
- deriv_eqOnproof · cited by 7
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- ModularForm.discriminant_qExpansion_coeff_oneproof · cited by 2
- derivWithin_tsumproof · cited by 1
- Complex.derivWithin_sqrtproof · cited by 0
- uniqueDiffWithinAt_Iooproof · cited by 0