Theorems · Theorem · general topology
LocallyFinite.comp_injective
∀ {ι : Type u_1} {ι' : Type u_2} {X : Type u_4} [inst : TopologicalSpace X] {f : ι → Set X} {g : ι' → ι},
LocallyFinite f → Function.Injective g → LocallyFinite (f ∘ g)- Defined in
- Mathlib.Topology.LocallyFinite
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Function.Injective.injOnproof · cited by 280
- LocallyFinitestatement and proof · cited by 141
- LocallyFinite.comp_injOnproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- precise_refinement_setproof · cited by 3
- LocallyFinite.iInter_compl_mem_nhdsproof · cited by 2
- contMDiff_finprod_condproof · cited by 1
- LocallyFinite.of_comp_surjectiveproof · cited by 1
- continuous_finprod_condproof · cited by 1
- Equiv.locallyFinite_comp_iffproof · cited by 1
- contMDiff_finsum_condproof · cited by 0
- continuous_finsum_condproof · cited by 0