OAI/Topology/CoarseAssembly/SeparatedUnion.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

A separated metric union

Components embed isometrically. Paths between different components go through chosen roots, with bridge length i + j + 2; thus bounded-distance cross-component pairs lie in finitely many finite components.

  1. theorem OAI.CoarseAssembly.separatedDist_same line 22
  2. theorem OAI.CoarseAssembly.separatedDist_different line 25
  3. theorem OAI.CoarseAssembly.separatedDist_comm line 30
  4. theorem OAI.CoarseAssembly.separatedDist_triangle line 40
  5. theorem OAI.CoarseAssembly.separatedDist_indices line 68