Theorems · Theorem · general topology
edist_dist
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y : α), edist x y = ENNReal.ofReal (dist x y)- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- ENNReal.ofRealstatement · cited by 863
- EDist.ediststatement · cited by 735
- PseudoMetricSpace.edist_distproof · cited by 3
Cited by39
Results whose statement or proof uses this declaration.
- edist_nndistproof · cited by 38
- edist_eq_enorm_subproof · cited by 37
- edist_lt_topproof · cited by 32
- dist_edistproof · cited by 21
- Set.Nontrivial.le_infsep_iffproof · cited by 6
- Metric.eball_ofRealproof · cited by 5
- MonotoneOn.eVariationOn_eqproof · cited by 4
- Metric.hausdorffEDist_ne_top_of_nonempty_of_boundedproof · cited by 4
- Metric.cthickening_singletonproof · cited by 4
- Metric.ediam_le_of_forall_dist_leproof · cited by 3
- hasFPowerSeriesOnBall_inverse_one_subproof · cited by 3
- Metric.mem_cthickening_of_dist_leproof · cited by 2