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Theorems · Theorem · general topology

IsLocallyConstant.comp

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] {f : X → Y},
  IsLocallyConstant f → ∀ (g : Y → Z), IsLocallyConstant (g ∘ f)
Defined in
Mathlib.Topology.LocallyConstant.Basic
Cited by
4 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
TopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsLocallyConstant.comp₂ · cited by 4IsLocallyConstant.comp₂Profinite.exists_locallyConstant · cited by 2Profinite.exists_locallyC…IsLocallyConstant.neg · cited by 0IsLocallyConstant.negIsLocallyConstant.inv · cited by 0IsLocallyConstant.invSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.preimage · cited by 4946Set.preimageIsOpen · cited by 2400IsOpenSet.preimage_comp · cited by 57Set.preimage_compIsLocallyConstant · cited by 51IsLocallyConstantIsLocallyConstant.compCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.