Mathlib Map

Theorems · Definition · general topology

AbstractCompletion.uniformStruct

{α : Type u} → [inst : UniformSpace α] → (self : AbstractCompletion.{v, u} α) → UniformSpace self.space

The completion carries a uniform structure.

Defined in
Mathlib.Topology.UniformSpace.AbstractCompletion
Cited by
30 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
UniformSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AbstractCompletion.uniformContinuous_coe · cited by 8AbstractCompletion.unifor…AbstractCompletion.isDenseInducing · cited by 7AbstractCompletion.isDens…AbstractCompletion.continuous_extend · cited by 5AbstractCompletion.contin…AbstractCompletion.dense · cited by 5AbstractCompletion.denseAbstractCompletion.funext · cited by 5AbstractCompletion.funextAbstractCompletion.uniformContinuous_extend · cited by 5AbstractCompletion.unifor…AbstractCompletion.extend_def · cited by 4AbstractCompletion.extend…AbstractCompletion.isUniformInducing · cited by 4AbstractCompletion.isUnif…AbstractCompletion.uniformContinuous_compare · cited by 4AbstractCompletion.unifor…AbstractCompletion.continuous_map · cited by 3AbstractCompletion.contin…LaurentSeries.valuation_compare · cited by 3LaurentSeries.valuation_c…AbstractCompletion.compareEquiv · cited by 2AbstractCompletion.compar…AbstractCompletion.induction_on · cited by 2AbstractCompletion.induct…AbstractCompletion.mapEquiv · cited by 2AbstractCompletion.mapEqu…AbstractCompletion.map_unique · cited by 2AbstractCompletion.map_un…UniformSpace · cited by 2040UniformSpaceAbstractCompletion.space · cited by 41AbstractCompletion.spaceAbstractCompletion · cited by 41AbstractCompletionAbstractCompletion.uniformStr…CITED BYCITES

Cites3

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

Cited by32

Results whose statement or proof uses this declaration.