Mathlib Map

Theorems · Theorem · general topology

IsUniformInducing.isInducing

∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β},
  IsUniformInducing f → Topology.IsInducing f
Defined in
Mathlib.Topology.UniformSpace.UniformEmbedding
Cited by
23 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpace

Around this declaration

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

IsUniformEmbedding.isEmbedding · cited by 25IsUniformEmbedding.isEmbe…IsUniformInducing.isDenseInducing · cited by 11IsUniformInducing.isDense…UniformSpace.Completion.isDenseInducing_coe · cited by 11Completion.isDenseInducin…AbstractCompletion.isDenseInducing · cited by 7AbstractCompletion.isDens…isComplete_image_iff · cited by 5isComplete_image_iffIsometry.comp_continuous_iff · cited by 5Isometry.comp_continuous_…IsUniformInducing.isUniformEmbedding · cited by 3IsUniformInducing.isUnifo…ArzelaAscoli.isCompact_of_equicontinuous · cited by 2ArzelaAscoli.isCompact_of…Isometry.comp_continuousOn_iff · cited by 2Isometry.comp_continuousO…ContinuousMap.tendsto_iff_tendstoUniformly · cited by 2ContinuousMap.tendsto_iff…ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM · cited by 1ContinuousAlternatingMap.…ContinuousMap.continuous_iff_continuous_uniformFun · cited by 1ContinuousMap.continuous_…IsUniformInducing.equicontinuousAt_iff · cited by 1IsUniformInducing.equicon…IsUniformInducing.equicontinuousWithinAt_iff · cited by 1IsUniformInducing.equicon…ContinuousLinearMap.isInducing_postcomp · cited by 1ContinuousLinearMap.isInd…UniformSpace · cited by 2040UniformSpaceTopology.IsInducing · cited by 266Topology.IsInducingIsUniformInducing · cited by 128IsUniformInducingTopology.IsInducing.induced · cited by 10IsInducing.inducedIsUniformInducing.comap_uniformSpace · cited by 4IsUniformInducing.comap_u…IsUniformInducing.isInducingCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by23

Results whose statement or proof uses this declaration.