Theorems · Theorem · algebraic topology

Topology.RelCWComplex.skeletonLT_inter_closedCell_eq_skeletonLT_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.skeletonLT C n) ∩ Topology.RelCWComplex.closedCell m j =
      ↑(Topology.RelCWComplex.skeletonLT C n) ∩ Topology.RelCWComplex.cellFrontier m j

A skeleton intersected with a closed cell of a higher dimension is the skeleton intersected with the boundary of the cell.

Defined in

Mathlib.Topology.CWComplex.Classical.Basic

Cited by

2 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2SpaceTopology.RelCWComplex