Theorems · Definition · general topology

Topology.Homeomorph.quotientKerEquivRange

Deprecated since 2026-07-10Use Homeomorph.quotientKerEquivRange instead.

{X : Type u_1} →
  {Y : Type u_2} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] → {f : X → Y} → Topology.IsStrictMap f → Quotient (Setoid.ker f) ≃ₜ ↑(Set.range f)

Alias of Homeomorph.quotientKerEquivRange. The homeomorphism Quotient (Setoid.ker f) ≃ₜ Set.range f given by a strict map f. This is the homeomorphism obtained from the first isomorphism theorem.

Defined in: Mathlib.Topology.Maps.Strict.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace

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Setstatement · cited by 53,352
TopologicalSpacestatement · cited by 24,529
Set.Elemstatement · cited by 7,166
Set.rangestatement · cited by 4,705
Homeomorphstatement · cited by 725
Topology.IsStrictMapstatement · cited by 45
Setoid.kerstatement · cited by 43
Homeomorph.quotientKerEquivRangeproof · cited by 0

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