OAI/Analysis/CircleDomains/Sobolev/SmoothJordanExhaustion.lean

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9 declarations, 0 contain sorry, 0 declared as axioms

A strict exhaustion by finite smooth Jordan cores

Every prescribed compact subset is retained in the interior of a finite Jordan core. Recursive application retains the preceding core and the next compact exhaustion set. The construction uses Sard, one-manifold classification, and Schoenflies.

  1. structure OAI.CircleDomainRigidity.SmoothJordanCore line 24
  2. def OAI.CircleDomainRigidity.SmoothJordanCore.carrier line 38
  3. theorem OAI.CircleDomainRigidity.SmoothJordanCore.isCompact line 40
  4. theorem OAI.CircleDomainRigidity.SmoothJordanCore.subset line 43
  5. theorem OAI.CircleDomainRigidity.SmoothJordanCore.regular line 45
  6. theorem OAI.CircleDomainRigidity.SmoothJordanCore.connected_interior line 48
  7. theorem OAI.CircleDomainRigidity.SmoothJordanCore.infty_interior line 52
  8. theorem OAI.CircleDomainRigidity.exists_smooth_jordan_core_containing line 60
  9. theorem OAI.CircleDomainRigidity.exists_smooth_jordan_exhaustion line 73