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Theorems · Definition · algebraic topology

Topology.RelCWComplex.skeleton

{X : Type u_1} →
  [t : TopologicalSpace X] →
    [T2Space X] →
      (C : Set X) → {D : Set X} → [inst : Topology.RelCWComplex C D] → ℕ∞ → Topology.RelCWComplex.Subcomplex C

The n-skeleton of a CW complex, for n ∈ ℕ ∪ {∞}. For statements use skeletonLT instead and then derive the statement about skeleton.

Defined in
Mathlib.Topology.CWComplex.Classical.Basic
Cited by
28 results in Mathlib
Foundations
Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceT2SpaceTopology.RelCWComplex

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Topology.RelCWComplex.skeleton_mono · cited by 2RelCWComplex.skeleton_monoTopology.RelCWComplex.openCell_subset_skeleton · cited by 2RelCWComplex.openCell_sub…Topology.RelCWComplex.closedCell_subset_skeleton · cited by 2RelCWComplex.closedCell_s…Topology.RelCWComplex.skeleton_inter_closedCell_eq_skeleton_inter_cellFrontier · cited by 1RelCWComplex.skeleton_int…Topology.RelCWComplex.skeleton_monotone · cited by 1RelCWComplex.skeleton_mon…Topology.RelCWComplex.skeleton_top · cited by 1RelCWComplex.skeleton_topTopology.RelCWComplex.skeleton_union_iUnion_closedCell_eq_skeleton_succ · cited by 1RelCWComplex.skeleton_uni…Topology.RelCWComplex.disjoint_skeleton_openCell · cited by 1RelCWComplex.disjoint_ske…Topology.RelCWComplex.iUnion_cellFrontier_subset_skeleton · cited by 1RelCWComplex.iUnion_cellF…Topology.RelCWComplex.iUnion_skeleton_eq_complex · cited by 1RelCWComplex.iUnion_skele…Topology.CWComplex.mem_skeleton_iff · cited by 1CWComplex.mem_skeleton_iffTopology.RelCWComplex.mem_skeleton_iff · cited by 1RelCWComplex.mem_skeleton…Topology.RelCWComplex.cellFrontier_subset_skeleton · cited by 1RelCWComplex.cellFrontier…Topology.CWComplex.disjoint_skeleton_openCell · cited by 0CWComplex.disjoint_skelet…Topology.CWComplex.skeleton_inter_closedCell_eq_skeleton_inter_cellFrontier · cited by 0CWComplex.skeleton_inter_…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceENat · cited by 4985ENatT2Space · cited by 1351T2SpaceTopology.RelCWComplex · cited by 195Topology.RelCWComplexTopology.RelCWComplex.Subcomplex · cited by 110RelCWComplex.SubcomplexTopology.RelCWComplex.skeletonLT · cited by 34RelCWComplex.skeletonLTRelCWComplex.skeletonCITED BYCITES

Cites7

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

Cited by28

Results whose statement or proof uses this declaration.