Theorems · Theorem · algebraic topology

Topology.RelCWComplex.finite_iff_finite_cells

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

A CW complex is finite iff the total number of its cells is finite.

Defined in: Mathlib.Topology.CWComplex.Classical.Finite
Cited by: 1 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Topology.RelCWComplex

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Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Finitestatement · cited by 3,029
Topology.RelCWComplexstatement and proof · cited by 195
Topology.RelCWComplex.cellstatement · cited by 194
Topology.RelCWComplex.Finitestatement and proof · cited by 11
Topology.RelCWComplex.finite_cells_of_finiteproof · cited by 2
Topology.RelCWComplex.finite_of_finite_cellsproof · cited by 2

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Topology.CWComplex.finite_iff_finite_cellsproof · cited by 0