Theorems · Theorem · convex and discrete geometry

PointedCone.isClosed_dual

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : PartialOrder R]
  [inst_2 : TopologicalSpace R] [ClosedIciTopology R] [inst_4 : IsOrderedRing R] [inst_5 : AddCommGroup M]
  [inst_6 : AddCommGroup N] [inst_7 : Module R M] [inst_8 : Module R N] [inst_9 : TopologicalSpace N]
  {p : M →ₗ[R] N →ₗ[R] R} {s : Set M}, (∀ (x : M), Continuous ⇑(p x)) → IsClosed ↑(PointedCone.dual p s)

Defined in

Mathlib.Analysis.Convex.Cone.Dual

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderTopologicalSpaceClosedIciTopologyIsOrderedRingAddCommGroupAddCommGroupModuleModuleTopologicalSpace