Theorems · Definition · functional analysis
AbsConvexOpenSets
(𝕜 : Type u_1) →
(E : Type u_2) →
[TopologicalSpace E] → [AddCommMonoid E] → [SeminormedRing 𝕜] → [SMul 𝕜 E] → [PartialOrder 𝕜] → Type (max 0 u_2)The type of absolutely convex open sets.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- IsOpenproof · cited by 2,400
- SeminormedRingstatement and proof · cited by 446
- AbsConvexproof · cited by 31
Cited by9
Results whose statement or proof uses this declaration.
- AbsConvexOpenSets.coe_isOpenstatement and proof · cited by 3
- gaugeSeminormFamilystatement and proof · cited by 3
- AbsConvexOpenSets.coe_zero_memstatement and proof · cited by 2
- AbsConvexOpenSets.coe_convexstatement and proof · cited by 1
- gaugeSeminormFamily_ballstatement and proof · cited by 1
- with_gaugeSeminormFamilystatement and proof · cited by 0
- AbsConvexOpenSets.coe_balancedstatement and proof · cited by 0
- AbsConvexOpenSets.coe_nhdsstatement and proof · cited by 0
- gaugeSeminormFamily.congr_simpstatement and proof · cited by 0