Theorems · Theorem · general topology
UniformSpace.mem_ball_self
∀ {α : Type ua} [inst : UniformSpace α] (x : α) {V : SetRel α α}, V ∈ uniformity α → x ∈ UniformSpace.ball x V- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 3 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.
Cites7
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 · cited by 765
- SetRelstatement and proof · cited by 581
- UniformSpace.ballstatement · cited by 113
- refl_mem_uniformityproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- IsCompact.uniformContinuousAt_of_continuousAtproof · cited by 1
- TendstoUniformlyOn.lowerHemicontinuousOnproof · cited by 1
- UniformSpace.nhds_basis_clopensproof · cited by 1