Theorems · Theorem · combinatorics

Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iff

∀ {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) ↔
    ∃ x, Topology.RelCWComplex.cellFrontier 1 e = Topology.RelCWComplex.closedCell 0 x

Defined in: Mathlib.Topology.CWComplex.Classical.Graph
Cited by: 1 results in Mathlib
Foundations: Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Topology.CWComplex

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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
Topology.RelCWComplex.cellstatement and proof · cited by 194
Topology.RelCWComplex.closedCellstatement and proof · cited by 70
Topology.RelCWComplex.cellFrontierstatement and proof · cited by 45
Topology.CWComplexstatement and proof · cited by 44
Set.union_selfproof · cited by 32
Graph.IsLoopAtstatement · cited by 29
Topology.CWComplex.OneSkeletonGraphstatement · cited by 8

Cited by1

Results whose statement or proof uses this declaration.

Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iff_subsingletonproof · cited by 1