Theorems · Theorem · general topology

isEmbedding_sumElim

∀ {X : Type u} {Y : Type v} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → Z} {g : Y → Z},
  Topology.IsEmbedding (Sum.elim f g) ↔
    Topology.IsEmbedding f ∧
      Topology.IsEmbedding g ∧
        Disjoint (closure (Set.range f)) (Set.range g) ∧ Disjoint (Set.range f) (closure (Set.range g))

Defined in

Mathlib.Topology.Constructions.SumProd

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace