Theorems · Theorem · functional analysis
AbsConvexOpenSets.coe_isOpen
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommMonoid E] [inst_2 : SeminormedRing 𝕜]
[inst_3 : SMul 𝕜 E] [inst_4 : PartialOrder 𝕜] (s : AbsConvexOpenSets 𝕜 E), IsOpen ↑s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- IsOpenstatement · cited by 2,400
- SeminormedRingstatement and proof · cited by 446
- AbsConvexstatement · cited by 31
- AbsConvexOpenSetsstatement and proof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- gaugeSeminormFamily_ballproof · cited by 1
- with_gaugeSeminormFamilyproof · cited by 0
- AbsConvexOpenSets.coe_nhdsproof · cited by 0