Theorems · Theorem · general topology
Metric.ball_subset_interior_closedBall
∀ {α : Type u} [inst : PseudoMetricSpace α] {x : α} {ε : ℝ}, Metric.ball x ε ⊆ interior (Metric.closedBall x ε)- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 119 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement · cited by 735
- interiorstatement · cited by 714
- Metric.closedBallstatement · cited by 704
- Metric.isOpen_ballproof · cited by 63
- Metric.ball_subset_closedBallproof · cited by 46
- interior_maximalproof · cited by 29
Cited by4
Results whose statement or proof uses this declaration.
- interior_closedBallproof · cited by 8
- IsUnifLocDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mulproof · cited by 3
- Besicovitch.exist_finset_disjoint_balls_large_measureproof · cited by 1
- Besicovitch.exists_closedBall_covering_tsum_measure_leproof · cited by 1