Theorems · Definition · general topology

Metric.gluePremetric

{X : Type u} →
  {Y : Type v} →
    {Z : Type w} →
      [Nonempty Z] →
        [inst : MetricSpace Z] →
          [inst_1 : MetricSpace X] →
            [inst_2 : MetricSpace Y] → {Φ : Z → X} → {Ψ : Z → Y} → Isometry Φ → Isometry Ψ → PseudoMetricSpace (X ⊕ Y)

Given two isometric embeddings Φ : Z → X and Ψ : Z → Y, we define a pseudometric space structure on X ⊕ Y by declaring that Φ x and Ψ x are at distance 0.

Defined in

Mathlib.Topology.MetricSpace.Gluing

Cited by

1 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonemptyMetricSpaceMetricSpaceMetricSpace