Theorems · Definition · general topology
SetRel.IsCover
{X : Type u_1} → SetRel X X → Set X → Set X → PropFor an entourage U, a set N is a `U`-cover of a set s if every point of s is U-close
to some point of N.
This is also called a `U`-net in the literature.
[R. Vershynin, High Dimensional Probability][vershynin2018high], 4.2.1.
- Defined in
- Mathlib.Data.Rel.Cover
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by19
Results whose statement or proof uses this declaration.
- Metric.IsCoverproof · cited by 51
- Dynamics.IsDynCoverOfproof · cited by 36
- SetRel.IsCover.mono_entouragestatement and proof · cited by 3
- UniformSpace.isCover_iff_subset_iUnion_ballstatement · cited by 3
- Dynamics.isDynCoverOf_zeroproof · cited by 2
- SetRel.IsCover.emptystatement · cited by 2
- SetRel.IsCover.nonemptystatement and proof · cited by 2
- SetRel.IsCover.of_subset_iUnion_ballstatement · cited by 2
- Dynamics.isDynCoverOf_univproof · cited by 1
- SetRel.IsCover.antistatement and proof · cited by 1
- SetRel.IsCover.monostatement and proof · cited by 1
- SetRel.IsCover.of_maximal_isSeparatedstatement · cited by 1