Theorems · Theorem · general topology
TopologicalSpace.Closeds.continuous_infEDist
∀ {α : Type u_1} [inst : EMetricSpace α], Continuous fun p => Metric.infEDist p.1 ↑p.2The edistance to a closed set depends continuously on the point and the set
- Defined in
- Mathlib.Topology.MetricSpace.Closeds
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- SetLike.coestatement and proof · cited by 8,199
- Continuousstatement · cited by 2,592
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- add_assocproof · cited by 746
- EDist.edistproof · cited by 735
- add_le_addproof · cited by 666
- EMetricSpacestatement and proof · cited by 242
- le_max_leftproof · cited by 215
- le_max_rightproof · cited by 205
- TopologicalSpace.Closedsstatement and proof · cited by 168
Cited by1
Results whose statement or proof uses this declaration.
- EMetric.continuous_infEdist_hausdorffEdistproof · cited by 0