Theorems · Theorem · global analysis
uniqueDiffWithinAt_iff_accPt
∀ {𝕜 : Type u_1} [inst : NormedDivisionRing 𝕜] {s : Set 𝕜} {x : 𝕜},
UniqueDiffWithinAt 𝕜 s x ↔ AccPt x (Filter.principal s)In one dimension, a point is a point of unique differentiability of a set iff it is an accumulation point of the set.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- SetLike.coeproof · cited by 8,199
- Submodule.spanproof · cited by 1,504
- Filter.principalstatement and proof · cited by 740
- NormedDivisionRingstatement and proof · cited by 360
- Denseproof · cited by 359
- UniqueDiffWithinAtstatement · cited by 252
- AccPtstatement and proof · cited by 75
- mem_closure_iff_clusterPtproof · cited by 16
- AccPt.clusterPtproof · cited by 6
- Submodule.span_univproof · cited by 6
- tangentConeAt_eq_univproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- AccPt.uniqueDiffWithinAtproof · cited by 4
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- range_derivWithin_subset_closure_span_imageproof · cited by 3
- Complex.derivWithin_const_cpowproof · cited by 1
- derivWithin_piproof · cited by 0