Theorems · Theorem · general topology
nhds_nhdsAdjoint
∀ {α : Type u} [inst : DecidableEq α] (a : α) (f : Filter α), nhds = Function.update pure a (pure a ⊔ f)- Defined in
- Mathlib.Topology.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- Function.updatestatement · cited by 502
- nhdsAdjointstatement · cited by 9
- Function.eq_update_iffproof · cited by 3
- nhds_nhdsAdjoint_of_neproof · cited by 2
- nhds_nhdsAdjoint_sameproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- WithZeroTopology.nhds_eq_updateproof · cited by 1
- le_nhdsAdjoint_iff'proof · cited by 0