Theorems · Theorem · algebraic topology

Topology.CWComplex.exists_cellFrontier_one_eq

∀ {X : Type u_1} [t : TopologicalSpace X] {C : Set X} [inst : Topology.CWComplex C]
  (e : Topology.RelCWComplex.cell C 1),
  ∃ x y,
    Topology.RelCWComplex.cellFrontier 1 e = Topology.RelCWComplex.closedCell 0 x ∪ Topology.RelCWComplex.closedCell 0 y

Defined in: Mathlib.Topology.CWComplex.Classical.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Topology.CWComplex

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Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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Set.union_singletonproof · cited by 107
Topology.RelCWComplex.closedCellstatement and proof · cited by 70
Topology.RelCWComplex.cellFrontierstatement and proof · cited by 45
Topology.RelCWComplex.mapproof · cited by 44

Cited by1

Results whose statement or proof uses this declaration.

Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iff_subsingletonproof · cited by 1