OAI/Geometry/SurfaceImmersion/Whitney/CrosscapPairModel.lean

GitHub source file

9 declarations, 0 contain sorry, 0 declared as axioms

The polynomial birth-and-death model for a pair of surface crosscaps. For a negative parameter it is an immersion on the whole coordinate plane.

  1. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPairCoordinates line 13
  2. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPairDerivative line 16
  3. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPairCoordinates_smooth line 21
  4. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPairCoordinates_hasFDerivAt line 26
  5. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPairDerivative_injective_iff line 43
  6. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPairCoordinates_singular_iff line 68
  7. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPair line 75
  8. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPair_smooth line 78
  9. theorem OAI.ClosedSurfaceR4.FiniteOrderSmoothing.crosscapPair_immersion_of_negative line 81