Theorems · Theorem · algebraic topology

Topology.RelCWComplex.skeletonLT_union_iUnion_closedCell_eq_skeletonLT_succ

∀ {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [inst : T2Space X] [inst_1 : Topology.RelCWComplex C D] (n : ℕ),
  ↑(Topology.RelCWComplex.skeletonLT C ↑n) ∪ ⋃ j, Topology.RelCWComplex.closedCell n j =
    ↑(Topology.RelCWComplex.skeletonLT C (↑n + 1))

Defined in: Mathlib.Topology.CWComplex.Classical.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 167 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 and proof · cited by 8,199
ENatstatement · cited by 4,985
Nat.cast_oneproof · cited by 2,501
Set.iUnionstatement and proof · cited by 2,483
T2Spacestatement and proof · cited by 1,351
Set.iUnion_congr_Propproof · cited by 374
Topology.RelCWComplexstatement and proof · cited by 195
Topology.RelCWComplex.cellstatement and proof · cited by 194
Topology.RelCWComplex.Subcomplexstatement · cited by 110
Topology.RelCWComplex.closedCellstatement and proof · cited by 70

Cited by2

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Topology.RelCWComplex.skeleton_union_iUnion_closedCell_eq_skeleton_succproof · cited by 1
Topology.CWComplex.skeletonLT_union_iUnion_closedCell_eq_skeletonLT_succproof · cited by 0