Theorems · Theorem · general topology
CauchySeq.nonempty
∀ {α : Type u} {β : Type v} [uniformSpace : UniformSpace α] [inst : Preorder β] {u : β → α}, CauchySeq u → Nonempty β- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpacePreorder
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.
- Preorderstatement and proof · cited by 7,952
- Filter.atTopproof · cited by 2,405
- UniformSpacestatement and proof · cited by 2,040
- CauchySeqstatement and proof · cited by 131
- Filter.nonempty_of_neBotproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- CauchySeq.mem_entourageproof · cited by 1