Theorems · Theorem · general topology
UniformSpace.hausdorff.uniformContinuous_union
∀ {α : Type u_1} [inst : UniformSpace α], UniformContinuous fun x => x.1 ∪ x.2- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
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.
- Setstatement and proof · cited by 53,352
- UniformSpacestatement and proof · cited by 2,040
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- uniformityproof · cited by 765
- UniformContinuousstatement · cited by 410
- hausdorffEntourageproof · cited by 35
- UniformSpace.hausdorffstatement · cited by 33
- Filter.mem_lift'proof · cited by 15
- entourageProdproof · cited by 12
- Filter.tendsto_lift'proof · cited by 5
- entourageProd_mem_uniformityproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.uniformContinuous_supproof · cited by 1
- TopologicalSpace.NonemptyCompacts.uniformContinuous_supproof · cited by 1
- TopologicalSpace.Closeds.uniformContinuous_supproof · cited by 1