Theorems · Theorem · general topology
nhdsGE_eq_iInf_inf_principal
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : Preorder α] [OrderTopology α] (a : α),
nhdsWithin a (Set.Ici a) = (⨅ u, ⨅ (_ : a < u), Filter.principal (Set.Iio u)) ⊓ Filter.principal (Set.Ici a)- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- LE.le.transproof · cited by 3,151
- le_antisymmproof · cited by 2,068
- nhdsWithinstatement · cited by 1,912
- iInfstatement and proof · cited by 1,690
- OrderTopologystatement and proof · cited by 1,355
- Set.Iiostatement and proof · cited by 1,166
- Set.Icistatement and proof · cited by 1,070
- Filter.principalstatement and proof · cited by 740
- inf_le_leftproof · cited by 286
Cited by1
Results whose statement or proof uses this declaration.
- nhdsGE_eq_iInf_principalproof · cited by 1