Theorems · Theorem · general topology
Filter.totallyBounded_map_iff
∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β} {F : Filter α},
IsUniformInducing f → ((Filter.map f F).TotallyBounded ↔ F.TotallyBounded)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceUniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.univproof · cited by 3,945
- UniformSpacestatement and proof · cited by 2,040
- Set.Finiteproof · cited by 1,814
- Filter.mapstatement and proof · cited by 819
- uniformityproof · cited by 765
- IsUniformInducingstatement and proof · cited by 128
- Filter.basis_setsproof · cited by 105
- Filter.univ_memproof · cited by 96
Cited by2
Results whose statement or proof uses this declaration.
- totallyBounded_image_iffproof · cited by 1
- Filter.totallyBounded_comapproof · cited by 0