Mathlib Map

Theorems · Definition · general topology

Metric.closedEBall

{α : Type u} → [PseudoEMetricSpace α] → α → ENNReal → Set α

Metric.closedEBall x ε is the set of all points y with edist y x ≤ ε

Defined in
Mathlib.Topology.EMetricSpace.Defs
Cited by
107 results in Mathlib
Foundations
Depth 107 from the axioms, rests on 1,992 definitions · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Metric.mem_closedEBall · cited by 7Metric.mem_closedEBallMetric.nhds_basis_closedEBall · cited by 5Metric.nhds_basis_closedE…Metric.eball_subset_closedEBall · cited by 5Metric.eball_subset_close…Metric.closedEBall_coe · cited by 4Metric.closedEBall_coeMetric.closedEBall_mem_nhds · cited by 4Metric.closedEBall_mem_nh…continuous_of_le_add_edist · cited by 4continuous_of_le_add_edistMetric.mem_closedEBall' · cited by 4Metric.mem_closedEBall'Metric.closedEBall_ofReal · cited by 3Metric.closedEBall_ofRealIsometry.preimage_closedEBall · cited by 3Isometry.preimage_closedE…Metric.closedEBall_top · cited by 3Metric.closedEBall_topMetric.ordConnected_setOfPred_closedEBall_subset · cited by 3Metric.ordConnected_setOf…Metric.preimage_smul_closedEBall · cited by 3Metric.preimage_smul_clos…Metric.preimage_vadd_closedEBall · cited by 3Metric.preimage_vadd_clos…IsometryEquiv.image_closedEBall · cited by 3IsometryEquiv.image_close…continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWith · cited by 3continuousOn_prod_of_subs…Set · cited by 53352SetENNReal · cited by 9879ENNRealSet.ofPred · cited by 6101Set.ofPredPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEDist.edist · cited by 735EDist.edistMetric.closedEBallCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by108

Results whose statement or proof uses this declaration.