Theorems · Theorem · general topology
comp_mem_uniformity_sets
∀ {α : Type ua} [inst : UniformSpace α] {s : SetRel α α}, s ∈ uniformity α → ∃ t ∈ uniformity α, SetRel.comp t t ⊆ s- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 63 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.
- Setstatement · cited by 53,352
- Filterstatement · cited by 8,121
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement and proof · cited by 765
- SetRelstatement and proof · cited by 581
- SetRel.compstatement · cited by 136
- monotone_idproof · cited by 31
- Filter.mem_lift'_setsproof · cited by 10
- Monotone.relCompproof · cited by 5
- comp_le_uniformityproof · cited by 4
Cited by18
Results whose statement or proof uses this declaration.
- comp_symm_mem_uniformity_setsproof · cited by 18
- comp_symm_of_uniformityproof · cited by 7
- CauchyFilter.denseRange_pureCauchyproof · cited by 5
- UniformSpace.subset_countable_closure_of_almost_dense_setproof · cited by 4
- comp3_mem_uniformityproof · cited by 4
- tendsto_comp_of_locally_uniform_limit_withinproof · cited by 3
- eventually_uniformity_iterate_comp_subsetproof · cited by 2
- UniformSpace.hausdorff.isClosed_setOfPred_totallyBoundedproof · cited by 2
- UniformSpace.hausdorff.isUniformInducing_closureproof · cited by 2
- UniformSpace.hausdorff.uniformContinuous_closureproof · cited by 2
- continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAtproof · cited by 2
- le_nhds_of_cauchy_adhp_auxproof · cited by 2