OAI/Geometry/SurfaceImmersion/Whitney/SmoothDoubleAtlas.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

The actual double-locus charts retain smooth coordinate expressions in both directions. Their overlap maps are ordinary smooth real functions.

  1. structure OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothDoubleChart line 15
  2. theorem OAI.ClosedSurfaceR4.FiniteOrderSmoothing.exists_smooth_double_chart line 30
  3. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothDoubleChart.overlap line 42
  4. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothDoubleChart.transition line 45
  5. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothDoubleChart.overlap_open line 48
  6. theorem OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothDoubleChart.transition_smooth line 52