Theorems · Definition · general topology
PairReduction.pairSetSeq
{T : Type u_1} → [PseudoEMetricSpace T] → [DecidableEq T] → Finset T → ENNReal → ENNReal → ℕ → Finset (T × T)Given a log-size ball sequence (Vᵢ, tᵢ, rᵢ), we define the pair set sequence by
Kᵢ = {tᵢ} × {x ∈ Vᵢ | dist(tᵢ, x) ≤ rᵢc}.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Finset.Nonemptyproof · cited by 1,001
- PairReduction.logSizeBallSeqproof · cited by 26
- PairReduction.logSizeBallStruct.pointproof · cited by 15
- Finset.productproof · cited by 6
- PairReduction.logSizeBallStruct.ballproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- PairReduction.pairSetproof · cited by 6
- PairReduction.card_pairSetSeq_le_logSizeRadius_mulstatement and proof · cited by 1
- PairReduction.card_pairSet_leproof · cited by 1
- PairReduction.edist_le_of_mem_pairSetproof · cited by 1
- PairReduction.iSup_edist_pairSetproof · cited by 1