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Theorems · Theorem · algebraic topology

Topology.CWComplex.finite_cells_of_finite

∀ {X : Type u_2} [inst : TopologicalSpace X] {C D : Set X} [inst_1 : Topology.RelCWComplex C D]
  [finite : Topology.RelCWComplex.Finite C], Finite ((n : ℕ) × Topology.RelCWComplex.cell C n)

Alias of Topology.RelCWComplex.finite_cells_of_finite. If C is finite as a CW complex then the collection of all cells (of any dimension) is finite.

Defined in
Mathlib.Topology.CWComplex.Classical.Finite
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Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopology.RelCWComplexTopology.RelCWComplex.Finite
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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceFinite · cited by 3029FiniteTopology.RelCWComplex · cited by 195Topology.RelCWComplexTopology.RelCWComplex.cell · cited by 194RelCWComplex.cellTopology.RelCWComplex.Finite · cited by 11RelCWComplex.FiniteTopology.RelCWComplex.finite_cells_of_finite · cited by 2RelCWComplex.finite_cells…CWComplex.finite_cells_of_fin…CITED BYCITES

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