Theorems · Theorem · general topology
comap_swap_uniformity
∀ {α : Type ua} [inst : UniformSpace α], Filter.comap Prod.swap (uniformity α) = uniformity α- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 8 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement · cited by 765
- Filter.comapstatement and proof · cited by 546
- Filter.comap_mapproof · cited by 12
- Prod.swap_injectiveproof · cited by 12
- uniformity_eq_symmproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- nhds_basis_uniformityproof · cited by 21
- symmetrize_mem_uniformityproof · cited by 11
- uniformity_eq_comap_nhds_zero_swappedproof · cited by 4
- uniformity_eq_comap_nhds_one_swappedproof · cited by 3
- uniformity_eq_comap_inv_mul_nhds_one_swappedproof · cited by 2
- uniformity_eq_comap_neg_add_nhds_zero_swappedproof · cited by 2
- uniformity_eq_comap_add_neg_nhds_zero_swappedproof · cited by 0
- uniformity_eq_comap_mul_inv_nhds_one_swappedproof · cited by 0