Theorems · Theorem · algebraic topology
Topology.RelCWComplex.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)If C is finite as a CW complex then the collection of all cells (of any dimension) is
finite.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Equivproof · cited by 8,337
- Filter.Eventuallyproof · cited by 3,134
- Finitestatement and proof · cited by 3,029
- Filter.atTopproof · cited by 2,405
- IsEmptyproof · cited by 759
- Topology.RelCWComplexstatement and proof · cited by 195
- Topology.RelCWComplex.cellstatement and proof · cited by 194
- Sigma.etaproof · cited by 25
- IsEmpty.falseproof · cited by 24
- Equiv.finite_iffproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- Topology.RelCWComplex.finite_iff_finite_cellsproof · cited by 1
- Topology.CWComplex.finite_cells_of_finiteproof · cited by 0