Theorems · Theorem · general topology
UniformSpace.mem_ball_comp
∀ {β : Type ub} {V W : Set (β × β)} {x y z : β},
y ∈ UniformSpace.ball x V → z ∈ UniformSpace.ball y W → z ∈ UniformSpace.ball x (SetRel.comp V W)The triangle inequality for UniformSpace.ball
- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetRel.compstatement · cited by 136
- UniformSpace.ballstatement and proof · cited by 113
- SetRel.prodMk_mem_compproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- UniformSpace.subset_countable_closure_of_almost_dense_setproof · cited by 4
- Dynamics.dynEntourage_comp_subsetproof · cited by 3
- UniformSpace.ball_subset_of_comp_subsetproof · cited by 1
- Dynamics.mem_ball_dynEntourage_compproof · cited by 1
- UniformSpace.completelyNormalSpace_of_hasAntitoneBasisproof · cited by 0