Theorems · Theorem · general topology
symmetrize_mem_uniformity
∀ {α : Type ua} [inst : UniformSpace α] {V : SetRel α α}, V ∈ uniformity α → V.symmetrize ∈ uniformity α- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 75 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement and proof · cited by 765
- SetRelstatement and proof · cited by 581
- Filter.setsproof · cited by 56
- SetRel.invproof · cited by 36
- Filter.preimage_mem_comapproof · cited by 23
- SetRel.symmetrizestatement · cited by 15
- comap_swap_uniformityproof · cited by 8
- Filter.inter_setsproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- comp_symm_mem_uniformity_setsproof · cited by 18
- UniformSpace.hasBasis_symmetricproof · cited by 5
- uniformity_hasBasis_open_symmetricproof · cited by 4
- Continuous.uniformContinuous_of_tendsto_cocompactproof · cited by 4
- Dynamics.coverEntropy_eq_iSup_netEntropyEntourageproof · cited by 2
- Dynamics.coverEntropy_image_of_comapproof · cited by 2
- TopologicalSpace.IsSeparable.exists_countable_dense_subsetproof · cited by 2
- Dynamics.coverEntropyInf_eq_iSup_netEntropyInfEntourageproof · cited by 2
- Dynamics.coverEntropyInf_image_of_comapproof · cited by 2
- UniformSpace.mem_nhds_iff_symmproof · cited by 0
- TotallyBounded.isSeparableproof · cited by 0