Theorems · Theorem · general topology

exists_seq_tendsto_sInf

∀ {α : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
  [FirstCountableTopology α] {S : Set α},
  S.Nonempty → BddBelow S → ∃ u, Antitone u ∧ Filter.Tendsto u Filter.atTop (nhds (sInf S)) ∧ ∀ (n : ℕ), u n ∈ S

Defined in

Mathlib.Topology.Order.IsLUB

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopologyFirstCountableTopology