Theorems · Theorem · general topology
nhdsSet_diagonal
∀ (X : Type u_4) [inst : TopologicalSpace (X × X)], nhdsSet (Set.diagonal X) = ⨆ x, nhds (x, x)
- Defined in
- Mathlib.Topology.NhdsSet
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- Set.imageproof · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- SupSet.sSupproof · cited by 954
- nhdsSetstatement · cited by 267
- Set.range_compproof · cited by 223
- Set.diagonalstatement and proof · cited by 42
- Function.diagproof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- nhdsSet_diagonal_le_uniformityproof · cited by 3
- compactSpace_uniformityproof · cited by 1