Theorems · Theorem · combinatorics

Topology.CWComplex.OneSkeletonGraph.not_exists_isLoopAt_iff_nontrivial

∀ {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).Nontrivial

Defined in: Mathlib.Topology.CWComplex.Classical.Graph
Cited by: 0 results in Mathlib
Foundations: Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Topology.CWComplex

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Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Iff.notproof · cited by 489
Topology.RelCWComplex.cellstatement and proof · cited by 194
Set.Nontrivialstatement · cited by 145
Topology.RelCWComplex.cellFrontierstatement · cited by 45
Topology.CWComplexstatement and proof · cited by 44
Graph.IsLoopAtstatement · cited by 29
Topology.CWComplex.OneSkeletonGraphstatement · cited by 8
Set.not_subsingleton_iffproof · cited by 7
Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iff_subsingletonproof · cited by 1

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