Theorems · Definition · algebraic topology
Topology.RelCWComplex.cellFrontier
{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 boundary of the n-cell given by the index i. Use this instead of map n i '' sphere 0 1
whenever possible.
- Cited by
- 45 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.sphereproof · cited by 371
- Topology.RelCWComplexstatement and proof · cited by 195
- Topology.RelCWComplex.cellstatement and proof · cited by 194
- Topology.RelCWComplex.mapproof · cited by 44
Cited by46
Results whose statement or proof uses this declaration.
- Topology.CWComplex.OneSkeletonGraphproof · cited by 8
- Topology.RelCWComplex.cellFrontier_subset_closedCellstatement · cited by 4
- Topology.RelCWComplex.cellFrontier_union_openCell_eq_closedCellstatement · cited by 4
- Topology.RelCWComplex.cellFrontier_subset_base_union_finite_closedCellstatement · cited by 3
- Topology.RelCWComplex.cellFrontier_subset_skeletonLTstatement and proof · cited by 3
- Topology.RelCWComplex.skeletonLT_inter_closedCell_eq_skeletonLT_inter_cellFrontierstatement and proof · cited by 2
- Topology.RelCWComplex.cellFrontier_one_eqstatement · cited by 2
- Topology.RelCWComplex.cellFrontier_zero_eq_emptystatement · cited by 2
- Topology.RelCWComplex.iUnion_cellFrontier_subset_skeletonLTstatement · cited by 2
- Topology.RelCWComplex.isClosed_cellFrontierstatement · cited by 2
- Topology.RelCWComplex.isClosed_inter_cellFrontier_succ_of_le_isClosed_inter_closedCellstatement and proof · cited by 2