Theorems · Definition · general topology
Metric.glueDist
{X : Type u} →
{Y : Type v} → {Z : Type w} → [MetricSpace X] → [MetricSpace Y] → (Z → X) → (Z → Y) → ℝ → X ⊕ Y → X ⊕ Y → ℝDefine a predistance on X ⊕ Y, for which Φ p and Ψ p are at distance ε
- Defined in
- Mathlib.Topology.MetricSpace.Gluing
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpaceMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- iInfproof · cited by 1,690
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
Cited by7
Results whose statement or proof uses this declaration.
- Metric.glueDist_glued_pointsstatement · cited by 2
- Metric.le_glueDist_inl_inrstatement · cited by 2
- Metric.gluePremetricproof · cited by 1
- Metric.le_glueDist_inr_inlstatement · cited by 1
- Metric.glueDist_swapstatement and proof · cited by 0
- Metric.Sum.dist_eq_glueDiststatement · cited by 0
- Metric.Sum.mem_uniformity_iff_glueDiststatement and proof · cited by 0