Mathlib Map

Theorems · Definition · general topology

UniformEquiv.symm

{α : Type u} → {β : Type u_1} → [inst : UniformSpace α] → [inst_1 : UniformSpace β] → α ≃ᵤ β → β ≃ᵤ α

Inverse of a uniform isomorphism.

Defined in
Mathlib.Topology.UniformSpace.Equiv
Cited by
28 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
UniformSpaceUniformSpace

Around this declaration

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

UniformEquiv.isUniformInducing · cited by 3UniformEquiv.isUniformInd…Padic.withValUniformEquiv · cited by 3Padic.withValUniformEquivAbstractCompletion.mapEquiv · cited by 2AbstractCompletion.mapEqu…UniformEquiv.apply_symm_apply · cited by 1UniformEquiv.apply_symm_a…UniformEquiv.arrowCongr · cited by 1UniformEquiv.arrowCongrIsDedekindDomain.HeightOneSpectrum.adicCompletion.continuous_ofCompletion · cited by 1adicCompletion.continuous…UniformEquiv.symm_apply_apply · cited by 1UniformEquiv.symm_apply_a…UniformEquiv.symm_comp_self · cited by 1UniformEquiv.symm_comp_se…AbstractCompletion.mapEquiv_symm · cited by 1AbstractCompletion.mapEqu…UniformEquiv.uniformContinuous_symm · cited by 1UniformEquiv.uniformConti…AbstractCompletion.uniformContinuous_compareEquiv_symm · cited by 1AbstractCompletion.unifor…UniformSpace.Completion.mapEquiv_symm · cited by 0Completion.mapEquiv_symmUniformEquiv.changeInv · cited by 0UniformEquiv.changeInvMetric.Snowflaking.uniformEquiv_symm_apply · cited by 0Snowflaking.uniformEquiv_…UniformEquiv.coe_symm_toEquiv · cited by 0UniformEquiv.coe_symm_toE…Equiv · cited by 8337EquivEquiv.symm · cited by 3681Equiv.symmUniformSpace · cited by 2040UniformSpaceUniformEquiv · cited by 80UniformEquivUniformEquiv.toEquiv · cited by 21UniformEquiv.toEquivUniformEquiv.uniformContinuous_invFun · cited by 1UniformEquiv.uniformConti…UniformEquiv.uniformContinuous_toFun · cited by 1UniformEquiv.uniformConti…UniformEquiv.symmCITED BYCITES

Cites7

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

Cited by33

Results whose statement or proof uses this declaration.