Theorems · Theorem · global analysis
uniqueDiffWithinAt_iff
∀ (R : Type u) {E : Type v} [inst : Semiring R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
[inst_3 : TopologicalSpace E] (s : Set E) (x : E),
UniqueDiffWithinAt R s x ↔ Dense ↑(Submodule.span R (tangentConeAt R s x)) ∧ x ∈ closure s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- Submodule.spanstatement and proof · cited by 1,504
- closurestatement and proof · cited by 1,254
- Densestatement and proof · cited by 359
- UniqueDiffWithinAtstatement and proof · cited by 252
- tangentConeAtstatement and proof · cited by 54
Cited by3
Results whose statement or proof uses this declaration.
- uniqueDiffWithinAt_univproof · cited by 16
- UniqueDiffWithinAt.monoproof · cited by 8
- UniqueDiffWithinAt.prodproof · cited by 4