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Theorems · Definition · global analysis

Diffeology.DSmooth

{X : Type u_1} → {Y : Type u_2} → [DiffeologicalSpace X] → [DiffeologicalSpace Y] → (X → Y) → Prop

A function between diffeological spaces is smooth iff composition with it preserves smoothness of plots.

Defined in
Mathlib.Geometry.Diffeology.Basic
Cited by
16 results in Mathlib
Foundations
Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DiffeologicalSpaceDiffeologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ContDiff.dSmooth · cited by 1ContDiff.dSmoothDiffeology.dSmooth_id · cited by 1Diffeology.dSmooth_idDiffeology.DSmooth.comp · cited by 1DSmooth.compDiffeology.DSmooth.contDiff · cited by 1DSmooth.contDiffDiffeology.DSmooth.continuous · cited by 1DSmooth.continuousDiffeology.DSmooth.isPlot · cited by 1DSmooth.isPlotDiffeology.IsPlot.dSmooth · cited by 1IsPlot.dSmoothDiffeology.dSmooth_const · cited by 0Diffeology.dSmooth_constDiffeology.dSmooth_id' · cited by 0Diffeology.dSmooth_id'Diffeology.dSmooth_iff · cited by 0Diffeology.dSmooth_iffDiffeology.dSmooth_iff_contDiff · cited by 0Diffeology.dSmooth_iff_co…Diffeology.DSmooth.comp' · cited by 0DSmooth.comp'Diffeology.DSmooth.continuous' · cited by 0DSmooth.continuous'Diffeology.isPlot_iff_dSmooth · cited by 0Diffeology.isPlot_iff_dSm…Diffeology.IsPlot.dSmooth_comp · cited by 0IsPlot.dSmooth_compReal · cited by 25697RealEuclideanSpace · cited by 307EuclideanSpaceDiffeologicalSpace · cited by 60DiffeologicalSpaceDiffeology.IsPlot · cited by 29Diffeology.IsPlotDiffeology.DSmoothCITED BYCITES

Cites4

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.