Theorems · Theorem · algebraic topology
Topology.RelCWComplex.closedCell_zero_eq_singleton
∀ {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [inst : Topology.RelCWComplex C D]
{j : Topology.RelCWComplex.cell C 0}, Topology.RelCWComplex.closedCell 0 j = {↑(Topology.RelCWComplex.map 0 j) ![]}- Cited by
- 4 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Nonemptyproof · cited by 2,627
- Matrix.vecEmptystatement and proof · cited by 832
- PartialEquiv.toFunstatement and proof · cited by 821
- Metric.closedBallproof · cited by 704
- Set.image_congrproof · cited by 533
- Topology.RelCWComplexstatement and proof · cited by 195
- Topology.RelCWComplex.cellstatement and proof · cited by 194
- Topology.RelCWComplex.closedCellstatement · cited by 70
- Topology.RelCWComplex.mapstatement and proof · cited by 44
Cited by4
Results whose statement or proof uses this declaration.
- Topology.CWComplex.closedCell_zero_eq_singletonproof · cited by 2
- Topology.RelCWComplex.closedCell_zero_injectiveproof · cited by 1
- Topology.CWComplex.exists_cellFrontier_one_eqproof · cited by 1