Theorems · Theorem · general topology

asymptoticCone_eq_closure_of_forall_smul_mem

∀ {k : Type u_1} {V : Type u_2} [inst : Field k] [inst_1 : LinearOrder k] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] [inst_4 : TopologicalSpace V] [inst_5 : TopologicalSpace k] [OrderTopology k]
  [IsStrictOrderedRing k] [IsTopologicalAddGroup V] [ContinuousSMul k V] {s : Set V},
  (∀ (c : k), 0 < c → ∀ x ∈ s, c • x ∈ s) → asymptoticCone k s = closure s

Defined in

Mathlib.Topology.Algebra.AsymptoticCone

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderAddCommGroupModuleTopologicalSpaceTopologicalSpaceOrderTopologyIsStrictOrderedRingIsTopologicalAddGroupContinuousSMul