Theorems · Theorem · algebraic topology

Topology.RelCWComplex.skeleton_inter_closedCell_eq_skeleton_inter_cellFrontier

∀ {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [inst : T2Space X] [inst_1 : Topology.RelCWComplex C D] {n : ℕ∞}
  {m : ℕ} {j : Topology.RelCWComplex.cell C m},
  n < ↑m →
    ↑(Topology.RelCWComplex.skeleton C n) ∩ Topology.RelCWComplex.closedCell m j =
      ↑(Topology.RelCWComplex.skeleton C n) ∩ Topology.RelCWComplex.cellFrontier m j

Version of skeletonLT_inter_closedCell_eq_skeletonLT_inter_cellFrontier using skeleton.

Defined in: Mathlib.Topology.CWComplex.Classical.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace T2Space Topology.RelCWComplex

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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
SetLike.coestatement · cited by 8,199
ENatstatement and proof · cited by 4,985
T2Spacestatement and proof · cited by 1,351
Topology.RelCWComplexstatement and proof · cited by 195
Topology.RelCWComplex.cellstatement and proof · cited by 194
Topology.RelCWComplex.Subcomplexstatement · cited by 110
Topology.RelCWComplex.closedCellstatement · cited by 70
Topology.RelCWComplex.cellFrontierstatement · cited by 45
Topology.RelCWComplex.skeletonstatement · cited by 28
Order.add_one_le_of_ltproof · cited by 13

Cited by1

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Topology.CWComplex.skeleton_inter_closedCell_eq_skeleton_inter_cellFrontierproof · cited by 0