Theorems · Theorem · general topology
nhds_bot_basis_Iic
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [inst_2 : OrderBot α] [OrderTopology α]
[Nontrivial α] [DenselyOrdered α], (nhds ⊥).HasBasis (fun a => ⊥ < a) Set.Iic- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- nhdsstatement · cited by 5,554
- Bot.botstatement and proof · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- OrderTopologystatement and proof · cited by 1,355
- Set.Iioproof · cited by 1,166
- Set.Iicstatement and proof · cited by 1,111
- OrderBotstatement and proof · cited by 1,055
- Filter.HasBasisstatement · cited by 604
- DenselyOrderedstatement and proof · cited by 471
- Filter.HasBasis.to_hasBasisproof · cited by 40
Cited by4
Results whose statement or proof uses this declaration.
- ENNReal.nhds_zero_basis_Iicproof · cited by 3
- Asymptotics.isLittleOTVS_iff_tendsto_divproof · cited by 2
- ENNReal.hasBasis_nhds_of_ne_top'proof · cited by 2
- EReal.nhdsWithin_botproof · cited by 1