Theorems · Definition · algebraic topology
Topology.RelCWComplex.openCell
{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 open n-cell given by the index i. Use this instead of map n i '' ball 0 1 whenever
possible.
- Cited by
- 75 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.ballproof · cited by 735
- Topology.RelCWComplexstatement and proof · cited by 195
- Topology.RelCWComplex.cellstatement and proof · cited by 194
- Topology.RelCWComplex.mapproof · cited by 44
Cited by84
Results whose statement or proof uses this declaration.
- Topology.RelCWComplex.openCell_subset_closedCellstatement · cited by 8
- Topology.RelCWComplex.disjoint_openCell_of_nestatement · cited by 6
- Topology.RelCWComplex.cellFrontier_union_openCell_eq_closedCellstatement and proof · cited by 4
- Topology.RelCWComplex.Subcomplex.closedCell_subset_of_memproof · cited by 4
- Topology.RelCWComplex.disjointBasestatement · cited by 4
- Topology.RelCWComplex.disjoint_skeletonLT_openCellstatement and proof · cited by 4
- Topology.RelCWComplex.closure_openCell_eq_closedCellstatement and proof · cited by 3
- Topology.RelCWComplex.Subcomplex.unionstatement · cited by 3
- Topology.RelCWComplex.Subcomplex.subset_complexproof · cited by 3
- Topology.RelCWComplex.map_zero_mem_openCellstatement · cited by 3
- Topology.RelCWComplex.openCell_zero_eq_singletonstatement · cited by 3