Mathlib Map

Theorems · Definition · general topology

AbstractCompletion.extend

{α : Type uα} →
  [inst : UniformSpace α] →
    (pkg : AbstractCompletion.{vα, uα} α) → {β : Type uβ} → [UniformSpace β] → (α → β) → pkg.space → β

Extension of maps to completions

Defined in
Mathlib.Topology.UniformSpace.AbstractCompletion
Cited by
12 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

UniformSpace.Completion.extension · cited by 16Completion.extensionAbstractCompletion.compare · cited by 8AbstractCompletion.compareAbstractCompletion.extend_coe · cited by 8AbstractCompletion.extend…AbstractCompletion.map · cited by 7AbstractCompletion.mapAbstractCompletion.continuous_extend · cited by 5AbstractCompletion.contin…AbstractCompletion.uniformContinuous_extend · cited by 5AbstractCompletion.unifor…AbstractCompletion.extend_def · cited by 4AbstractCompletion.extend…AbstractCompletion.extension₂_coe_coe · cited by 2AbstractCompletion.extens…AbstractCompletion.map_unique · cited by 2AbstractCompletion.map_un…AbstractCompletion.uniformContinuous_extension₂ · cited by 2AbstractCompletion.unifor…AbstractCompletion.extend₂ · cited by 2AbstractCompletion.extend₂AbstractCompletion.isUniformInducing_extend · cited by 1AbstractCompletion.isUnif…AbstractCompletion.extend_comp_coe · cited by 1AbstractCompletion.extend…AbstractCompletion.extend_map · cited by 1AbstractCompletion.extend…AbstractCompletion.extend_unique · cited by 1AbstractCompletion.extend…UniformSpace · cited by 2040UniformSpaceUniformContinuous · cited by 410UniformContinuousAbstractCompletion.space · cited by 41AbstractCompletion.spaceAbstractCompletion · cited by 41AbstractCompletionIsDenseInducing.extend · cited by 29IsDenseInducing.extendAbstractCompletion.isDenseInducing · cited by 7AbstractCompletion.isDens…AbstractCompletion.dense · cited by 5AbstractCompletion.denseDenseRange.some · cited by 1DenseRange.someAbstractCompletion.extendCITED BYCITES

Cites8

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

Cited by16

Results whose statement or proof uses this declaration.