Theorems · Theorem · algebraic topology

Topology.CWComplex.isClosed_of_isClosed_inter_openCell_or_isClosed_inter_closedCell

∀ {X : Type u_1} [t : TopologicalSpace X] {C : Set X} [inst : Topology.CWComplex C] [T2Space X] {A : Set X},
  A ⊆ C →
    (∀ (n : ℕ),
        0 < n →
          ∀ (j : Topology.RelCWComplex.cell C n),
            IsClosed (A ∩ Topology.RelCWComplex.openCell n j) ∨ IsClosed (A ∩ Topology.RelCWComplex.closedCell n j)) →
      IsClosed A

If for every cell either A ∩ openCell n j or A ∩ closedCell n j is closed then A is closed.

Defined in

Mathlib.Topology.CWComplex.Classical.Basic

Cited by

0 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopology.CWComplexT2Space