Mathlib Map

Theorems · Theorem · algebraic topology

Topology.CWComplex.finite_of_finite_cells

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

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

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

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

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_of_finite_cells · cited by 2RelCWComplex.finite_of_fi…CWComplex.finite_of_finite_ce…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.