Theorems · Theorem · algebraic topology

Topology.RelCWComplex.closure_openCell_eq_closedCell

∀ {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [inst : Topology.RelCWComplex C D] [T2Space X] {n : ℕ}
  {j : Topology.RelCWComplex.cell C n},
  closure (Topology.RelCWComplex.openCell n j) = Topology.RelCWComplex.closedCell n j

Defined in: Mathlib.Topology.CWComplex.Classical.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Topology.RelCWComplex T2Space

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Cites21

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
Realproof · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
Set.imageproof · cited by 5,609
ContinuousOnproof · cited by 1,411
T2Spacestatement and proof · cited by 1,351
closurestatement and proof · cited by 1,254
one_ne_zeroproof · cited by 885
PartialEquiv.toFunproof · cited by 821
Topology.RelCWComplexstatement and proof · cited by 195
Topology.RelCWComplex.cellstatement and proof · cited by 194
subset_antisymmproof · cited by 150

Cited by3

Results whose statement or proof uses this declaration.

Topology.RelCWComplex.Subcomplex.closedCell_subset_of_memproof · cited by 4
Topology.RelCWComplex.disjoint_interior_base_closedCellproof · cited by 1
Topology.CWComplex.closure_openCell_eq_closedCellproof · cited by 0