Theorems · Theorem · general topology

Topology.IsQuotientMap.of_comp_of_isCoinducing

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {f : X → Y} {g : Y → Z} [inst : TopologicalSpace X]
  [inst_1 : TopologicalSpace Y] [inst_2 : TopologicalSpace Z],
  Topology.IsQuotientMap (g ∘ f) → Topology.IsCoinducing f → Topology.IsQuotientMap g

Defined in: Mathlib.Topology.Maps.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace TopologicalSpace

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Cites7

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

TopologicalSpacestatement and proof · cited by 24,529
Topology.IsQuotientMapstatement and proof · cited by 124
Topology.IsQuotientMap.isCoinducingproof · cited by 35
Topology.IsCoinducingstatement and proof · cited by 31
Function.Surjective.of_compproof · cited by 30
Topology.IsQuotientMap.surjectiveproof · cited by 24
Topology.IsCoinducing.of_comp_iffproof · cited by 3

Cited by2

Results whose statement or proof uses this declaration.

Topology.IsQuotientMap.of_comp_isQuotientMapproof · cited by 2
Topology.IsQuotientMap.of_comp_of_eq_coinducedproof · cited by 0