Theorems · Theorem · combinatorics

Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iff_subsingleton

∀ {X : Type u_1} [inst : TopologicalSpace X] {C : Set X} [inst_1 : Topology.CWComplex C]
  (e : Topology.RelCWComplex.cell C 1),
  (∃ x, (Topology.CWComplex.OneSkeletonGraph C).IsLoopAt e x) ↔ (Topology.RelCWComplex.cellFrontier 1 e).Subsingleton

Defined in: Mathlib.Topology.CWComplex.Classical.Graph
Cited by: 1 results in Mathlib
Foundations: Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Topology.CWComplex

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

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
Matrix.vecEmptyproof · cited by 832
PartialEquiv.toFunproof · cited by 821
Set.Subsingletonstatement and proof · cited by 276
Topology.RelCWComplex.cellstatement and proof · cited by 194
Set.insert_eq_of_memproof · cited by 118
Set.union_singletonproof · cited by 107
Topology.RelCWComplex.closedCellproof · cited by 70
Topology.RelCWComplex.cellFrontierstatement and proof · cited by 45
Topology.RelCWComplex.mapproof · cited by 44
Topology.CWComplexstatement and proof · cited by 44

Cited by1

Results whose statement or proof uses this declaration.

Topology.CWComplex.OneSkeletonGraph.not_exists_isLoopAt_iff_nontrivialproof · cited by 0