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Theorems · Theorem · general topology

induced_compose

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {tγ : TopologicalSpace γ} {f : α → β} {g : β → γ},
  TopologicalSpace.induced f (TopologicalSpace.induced g tγ) = TopologicalSpace.induced (g ∘ f) tγ
Defined in
Mathlib.Topology.Order
Cited by
26 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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continuous_induced_rng · cited by 38continuous_induced_rngTopology.IsInducing.comp · cited by 17IsInducing.compTopologicalSpace.NonemptyCompacts.isEmbedding_toCompacts · cited by 12NonemptyCompacts.isEmbedd…Topology.IsInducing.of_comp · cited by 11IsInducing.of_compTopology.IsInducing.of_comp_iff · cited by 5IsInducing.of_comp_iffPi.induced_precomp' · cited by 2Pi.induced_precomp'TopCat.prod_topology · cited by 2TopCat.prod_topologyUniformOnFun.continuousSMul_induced_of_image_bounded · cited by 2UniformOnFun.continuousSM…induced_to_pi · cited by 2induced_to_piLinearMap.isInducing_of_restrict_nhds_zero · cited by 1LinearMap.isInducing_of_r…IsModuleTopology.isoₛₗ · cited by 1IsModuleTopology.isoₛₗAddUnits.topology_eq_inf · cited by 1AddUnits.topology_eq_infTopCat.pullback_topology · cited by 1TopCat.pullback_topologyTopCat.isInducing_prodMap · cited by 1TopCat.isInducing_prodMapTopCat.isInducing_pullback_to_prod · cited by 1TopCat.isInducing_pullbac…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.preimage · cited by 4946Set.preimageIsOpen · cited by 2400IsOpenTopologicalSpace.induced · cited by 148TopologicalSpace.inducedTopologicalSpace.ext · cited by 15TopologicalSpace.extinduced_composeCITED BYCITES

Cites6

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Cited by26

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