Theorems · Theorem · general topology
edist_ne_top_of_mem_ball
∀ {β : Type u_2} [inst : EMetricSpace β] {a : β} {r : ENNReal} (x y : ↑(Metric.eball a r)), edist ↑x ↑y ≠ ⊤In an emetric ball, the distance between points is everywhere finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- Set.Elemstatement and proof · cited by 7,166
- EDist.ediststatement and proof · cited by 735
- le_topproof · cited by 411
- Metric.eballstatement and proof · cited by 294
- EMetricSpacestatement and proof · cited by 242
- ne_of_ltproof · cited by 203
- PseudoEMetricSpace.edist_commproof · cited by 52
- ENNReal.add_lt_addproof · cited by 13
- edist_triangle_leftproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- metricSpaceEMetricBallproof · cited by 0