Theorems · Theorem · general topology

IsLocalHomeomorph.of_comp

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

Defined in: Mathlib.Topology.IsLocalHomeomorph
Cited by: 1 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace TopologicalSpace

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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
Set.univproof · cited by 3,945
Continuousstatement and proof · cited by 2,592
Continuous.continuousAtproof · cited by 297
IsLocalHomeomorphstatement and proof · cited by 35
IsLocalHomeomorph.isLocalHomeomorphOnproof · cited by 6
isLocalHomeomorph_iff_isLocalHomeomorphOn_univproof · cited by 5
IsLocalHomeomorphOn.of_comp_leftproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

IsLocalHomeomorph.isOpenEmbedding_of_compproof · cited by 1