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Theorems · Theorem · convex and discrete geometry

strictConvex_singleton

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : TopologicalSpace E]
  [inst_3 : AddCommMonoid E] [inst_4 : Module 𝕜 E] (c : E), StrictConvex 𝕜 {c}
Defined in
Mathlib.Analysis.Convex.Strict
Cited by
1 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
SemiringPartialOrderTopologicalSpaceAddCommMonoidModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

StrictConvex.add_left · cited by 2StrictConvex.add_leftSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderinterior · cited by 714interiorStrictConvex · cited by 71StrictConvexSet.pairwise_singleton · cited by 7Set.pairwise_singletonstrictConvex_singletonCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.