Mathlib Map

Theorems · Definition · general topology

ContinuousMap.id

(α : Type u_1) → [inst : TopologicalSpace α] → C(α, α)

The identity as a continuous map.

Defined in
Mathlib.Topology.ContinuousMap.Basic
Cited by
73 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
TopologicalSpace
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Around this declaration

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

ContinuousMapZero.id · cited by 23ContinuousMapZero.idTopCat.Homotopy.h · cited by 15Homotopy.hBoundedContinuousFunction.domRestrict · cited by 12BoundedContinuousFunction…cfcHom_id · cited by 11cfcHom_idIsCoveringMap.liftHomotopy · cited by 6IsCoveringMap.liftHomotopyContinuousFunctionalCalculus.exists_cfc_of_predicate · cited by 5ContinuousFunctionalCalcu…NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate · cited by 5NonUnitalContinuousFuncti…cfcHom_eq_of_continuous_of_map_id · cited by 5cfcHom_eq_of_continuous_o…CocompactMap.id · cited by 5CocompactMap.idContinuousOpenMap.id · cited by 4ContinuousOpenMap.idReal.Lp.fourierTransformInv · cited by 4Lp.fourierTransformInvPath.id · cited by 2Path.idContinuousMap.comp_id · cited by 2ContinuousMap.comp_idRCLike.nonUnitalContinuousFunctionalCalculus · cited by 2RCLike.nonUnitalContinuou…Matrix.IsHermitian.cfcAux_id · cited by 2IsHermitian.cfcAux_idTopologicalSpace · cited by 24529TopologicalSpaceContinuousMap · cited by 2491ContinuousMapContinuousMap.idCITED BYCITES

Cites2

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

Cited by103

Results whose statement or proof uses this declaration.