Theorems · Theorem · general topology

IsLUB.exists_seq_monotone_tendsto

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] {t : Set α} {x : α}
  [(nhds x).IsCountablyGenerated],
  IsLUB t x →
    t.Nonempty → ∃ u, Monotone u ∧ (∀ (n : ℕ), u n ≤ x) ∧ Filter.Tendsto u Filter.atTop (nhds x) ∧ ∀ (n : ℕ), u n ∈ t

Defined in

Mathlib.Topology.Order.IsLUB

Cited by

3 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyFilter.IsCountablyGenerated