Mathlib Map

Theorems · Theorem · general topology

AbstractCompletion.isUniformInducing_extend

∀ {α : Type uα} [inst : UniformSpace α] (pkg : AbstractCompletion.{vα, uα} α) {β : Type uβ} [inst_1 : UniformSpace β]
  {f : α → β} [CompleteSpace β], IsUniformInducing f → IsUniformInducing (pkg.extend f)
Defined in
Mathlib.Topology.UniformSpace.AbstractCompletion
Cited by
1 results in Mathlib
Foundations
Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpaceCompleteSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

UniformSpace.Completion.isUniformInducing_extension · cited by 0Completion.isUniformInduc…CompleteSpace · cited by 2532CompleteSpaceUniformSpace · cited by 2040UniformSpaceIsUniformInducing · cited by 128IsUniformInducingAbstractCompletion · cited by 41AbstractCompletionAbstractCompletion.space · cited by 41AbstractCompletion.spaceIsUniformInducing.uniformContinuous · cited by 35IsUniformInducing.uniform…AbstractCompletion.uniformStruct · cited by 30AbstractCompletion.unifor…AbstractCompletion.extend · cited by 12AbstractCompletion.extendAbstractCompletion.isDenseInducing · cited by 7AbstractCompletion.isDens…AbstractCompletion.extend_def · cited by 4AbstractCompletion.extend…AbstractCompletion.isUniformInducing · cited by 4AbstractCompletion.isUnif…IsDenseInducing.isUniformInducing_extend · cited by 1IsDenseInducing.isUniform…AbstractCompletion.isUniformI…CITED BYCITES

Cites12

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

Cited by1

Results whose statement or proof uses this declaration.