Theorems · Definition · algebraic topology
Topology.RelCWComplex.closedCell
{X : Type u_1} →
[t : TopologicalSpace X] →
{C D : Set X} → [inst : Topology.RelCWComplex C D] → (n : ℕ) → Topology.RelCWComplex.cell C n → Set XThe closed n-cell given by the index i. Use this instead of map n i '' closedBall 0 1
whenever possible.
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.imageproof · cited by 5,609
- PartialEquiv.toFunproof · cited by 821
- Metric.closedBallproof · cited by 704
- Topology.RelCWComplexstatement and proof · cited by 195
- Topology.RelCWComplex.cellstatement and proof · cited by 194
- Topology.RelCWComplex.mapproof · cited by 44
Cited by74
Results whose statement or proof uses this declaration.
- Topology.RelCWComplex.skeletonLTproof · cited by 34
- Topology.CWComplex.OneSkeletonGraphproof · cited by 8
- Topology.RelCWComplex.coe_skeletonLTstatement · cited by 8
- Topology.RelCWComplex.openCell_subset_closedCellstatement · cited by 8
- Topology.RelCWComplex.skeletonLT_monoproof · cited by 4
- Topology.RelCWComplex.Subcomplex.closedCell_subset_of_memstatement · cited by 4
- Topology.RelCWComplex.cellFrontier_subset_closedCellstatement · cited by 4
- Topology.RelCWComplex.cellFrontier_union_openCell_eq_closedCellstatement and proof · cited by 4
- Topology.RelCWComplex.closedCell_subset_complexstatement and proof · cited by 4
- Topology.RelCWComplex.closedCell_zero_eq_singletonstatement · cited by 4
- Topology.RelCWComplex.isClosed_closedCellstatement · cited by 4
- Topology.RelCWComplex.cellFrontier_subset_base_union_finite_closedCellstatement · cited by 3