Theorems · Theorem · general topology
IsLUB.exists_seq_strictMono_tendsto_of_notMem
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] {t : Set α} {x : α}
[(nhds x).IsCountablyGenerated],
IsLUB t x →
x ∉ t →
t.Nonempty →
∃ u, StrictMono 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
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- Set.Nonemptystatement and proof · cited by 2,627
- Filter.atTopstatement and proof · cited by 2,405
- nhdsWithinproof · cited by 1,912
- OrderTopologystatement and proof · cited by 1,355
- Set.Iicproof · cited by 1,111
- Nat.iterateproof · cited by 740
Cited by4
Results whose statement or proof uses this declaration.
- exists_seq_strictMono_tendsto'proof · cited by 6
- IsLUB.exists_seq_monotone_tendstoproof · cited by 3
- Dense.exists_seq_strictMono_tendsto_of_ltproof · cited by 3
- IsGLB.exists_seq_strictAnti_tendsto_of_notMemproof · cited by 0