OAI/Topology/CoarseAssembly/AmpleRipsFamily.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

Spatial representatives for finite-Rips families on the fixed ample module

The source Hilbert spaces may vary with the component. Each is embedded isometrically into ℓ²(ℕ, ℂ), and the operator is extended by the identity. The compact square defects give one whole-union boundary class.

  1. theorem OAI.CoarseAssembly.Rips.ampleRipsOperator_norm_le line 24
  2. theorem OAI.CoarseAssembly.Rips.ampleRipsOperator_selfAdjoint line 29
  3. theorem OAI.CoarseAssembly.Rips.ampleRipsOperator_propagation line 34
  4. theorem OAI.CoarseAssembly.Rips.ampleRipsOperator_square_compact line 39