Theorems · Theorem · algebraic topology
Topology.RelCWComplex.injective_map_zero
∀ {X : Type u_1} [t : TopologicalSpace X] {D : Set X} (C : Set X) [inst : Topology.RelCWComplex C D],
Function.Injective fun x => ↑(Topology.RelCWComplex.map 0 x) ![]If two 0-cells have the same characteristic image point, they are equal.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Matrix.vecEmptystatement and proof · cited by 832
- PartialEquiv.toFunstatement and proof · cited by 821
- Topology.RelCWComplexstatement and proof · cited by 195
- Topology.RelCWComplex.cellstatement and proof · cited by 194
- Topology.RelCWComplex.mapstatement and proof · cited by 44
- Set.not_disjoint_iffproof · cited by 30
- Topology.RelCWComplex.disjoint_openCell_of_neproof · cited by 6
- Topology.RelCWComplex.openCell_zero_eq_singletonproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iff_subsingletonproof · cited by 1
- Topology.RelCWComplex.map_zero_eq_self_iffproof · cited by 1
- Topology.RelCWComplex.openCell_zero_injectiveproof · cited by 1
- Topology.RelCWComplex.closedCell_zero_injectiveproof · cited by 1
- Topology.CWComplex.injective_map_zeroproof · cited by 0