Theorems · Definition · general topology
nhdsAdjoint
{α : Type u} → α → Filter α → TopologicalSpace αThis construction is left adjoint to the operation sending a topology on α
to its neighborhood filter at a fixed point a : α.
- Defined in
- Mathlib.Topology.Order
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- Filterstatement and proof · cited by 8,121
- Set.univproof · cited by 3,945
- Filter.univ_memproof · cited by 96
Cited by10
Results whose statement or proof uses this declaration.
- WithZeroTopology.topologicalSpaceproof · cited by 27
- gc_nhdsstatement and proof · cited by 8
- nhds_nhdsAdjointstatement · cited by 2
- nhds_nhdsAdjoint_of_nestatement and proof · cited by 2
- continuous_nhdsAdjoint_domstatement · cited by 1
- isOpen_singleton_nhdsAdjointstatement · cited by 1
- nhds_nhdsAdjoint_samestatement and proof · cited by 1
- le_nhdsAdjoint_iffstatement · cited by 0
- le_nhdsAdjoint_iff'statement and proof · cited by 0
- coinduced_nhdsAdjointstatement and proof · cited by 0