Theorems · Theorem · general topology
Metric.Snowflaking.image_toSnowflaking_closedEBall
∀ {X : Type u_1} {α : ℝ} {hα₀ : 0 < α} {hα₁ : α ≤ 1} [inst : PseudoEMetricSpace X] (x : X) (r : ENNReal),
⇑Metric.Snowflaking.toSnowflaking '' Metric.closedEBall x r =
Metric.closedEBall (Metric.Snowflaking.toSnowflaking x) (r ^ α)- Defined in
- Mathlib.Topology.MetricSpace.Snowflaking
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Equivstatement · cited by 8,337
- Set.imagestatement · cited by 5,609
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Metric.closedEBallstatement and proof · cited by 107
- Metric.Snowflakingstatement and proof · cited by 65
- Metric.Snowflaking.toSnowflakingstatement and proof · cited by 41
- Metric.Snowflaking.image_toSnowflaking_eq_preimageproof · cited by 6
- Metric.Snowflaking.preimage_ofSnowflaking_closedEBallproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Metric.Snowflaking.preimage_toSnowflaking_closedEBallproof · cited by 2
- Metric.Snowflaking.image_toSnowflaking_emetricClosedBallproof · cited by 0