Theorems · Theorem · general topology

isQuotientMap_of_isOpenQuotientMap_of_isInducing

∀ {A : Type u_4} {B : Type u_5} {C : Type u_6} {D : Type u_7} [inst : TopologicalSpace A] [inst_1 : TopologicalSpace B]
  [inst_2 : TopologicalSpace C] [inst_3 : TopologicalSpace D] (f : A → B) (g : C → D) (p : A → C) (q : B → D),
  g ∘ p = q ∘ f →
    Topology.IsInducing f →
      Function.Surjective p →
        IsOpenQuotientMap q → Topology.IsEmbedding g → q ⁻¹' q '' Set.range f ⊆ Set.range f → Topology.IsQuotientMap p

Defined in: Mathlib.Topology.Maps.OpenQuotient
Cited by: 0 results in Mathlib
Foundations: Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace TopologicalSpace TopologicalSpace

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Set.imagestatement and proof · cited by 5,609
Set.preimagestatement and proof · cited by 4,946
Set.rangestatement and proof · cited by 4,705
Topology.IsEmbeddingstatement and proof · cited by 294
Topology.IsInducingstatement and proof · cited by 266
Topology.IsQuotientMapstatement · cited by 124
Topology.IsEmbedding.injectiveproof · cited by 103
IsOpenQuotientMapstatement and proof · cited by 65
Topology.IsEmbedding.toIsInducingproof · cited by 48
Topology.IsInducing.eq_inducedproof · cited by 31

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