Theorems · Theorem · general topology

Dense.exists_seq_strictMono_tendsto

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α]
  [NoMinOrder α] [FirstCountableTopology α] {s : Set α},
  Dense s → ∀ (x : α), ∃ u, StrictMono u ∧ (∀ (n : ℕ), u n ∈ Set.Iio x ∩ s) ∧ Filter.Tendsto u Filter.atTop (nhds x)

Defined in

Mathlib.Topology.Order.IsLUB

Cited by

2 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyDenselyOrderedNoMinOrderFirstCountableTopology