Theorems · Theorem · general topology
isRefl_of_mem_uniformity
∀ {α : Type ua} [inst : UniformSpace α] {s : SetRel α α}, s ∈ uniformity α → s.IsRefl- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 64 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.
Cites6
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 and proof · cited by 765
- SetRelstatement and proof · cited by 581
- SetRel.IsReflstatement · cited by 26
- refl_mem_uniformityproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- comp3_mem_uniformityproof · cited by 4
- eventually_uniformity_iterate_comp_subsetproof · cited by 2
- lift'_comp_uniformityproof · cited by 2
- Dynamics.coverEntropy_eq_iSup_netEntropyEntourageproof · cited by 2
- Dynamics.coverEntropyInf_eq_iSup_netEntropyInfEntourageproof · cited by 2
- subset_comp_self_of_mem_uniformityproof · cited by 1