Theorems · Theorem · general topology
Metric.isClosed_closedBall
∀ {α : Type u_2} [inst : PseudoMetricSpace α] {x : α} {ε : ℝ}, IsClosed (Metric.closedBall x ε)- Cited by
- 28 results in Mathlib
- Foundations
- Depth 155 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- IsClosedstatement · cited by 1,639
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- continuous_id'proof · cited by 295
- continuous_constproof · cited by 278
- isClosed_leproof · cited by 32
- Continuous.distproof · cited by 20
Cited by28
Results whose statement or proof uses this declaration.
- measurableSet_closedBallproof · cited by 13
- Metric.closure_ball_subset_closedBallproof · cited by 10
- Metric.closedBall_zero'proof · cited by 4
- Metric.closure_closedBallproof · cited by 3
- ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverseproof · cited by 3
- ProperSpace.of_seq_closedBallproof · cited by 2
- IsUltrametricDist.isClopen_closedBallproof · cited by 2
- Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_auxproof · cited by 1
- SmoothBumpFunction.isClosed_image_of_isClosedproof · cited by 1
- NormedAddCommGroup.exists_norm_nsmul_leproof · cited by 1
- tendsto_integral_comp_smul_smul_of_integrableproof · cited by 1
- ae_eq_const_or_norm_average_lt_of_norm_le_constproof · cited by 1