Theorems · Theorem · algebraic topology

Topology.RelCWComplex.cellFrontier_union_openCell_eq_closedCell

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

Defined in: Mathlib.Topology.CWComplex.Classical.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Topology.RelCWComplex

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Cites15

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
Set.imageproof · cited by 5,609
PartialEquiv.toFunproof · cited by 821
Metric.ballproof · cited by 735
Metric.closedBallproof · cited by 704
Metric.sphereproof · cited by 371
Topology.RelCWComplexstatement and proof · cited by 195
Topology.RelCWComplex.cellstatement and proof · cited by 194
Topology.RelCWComplex.openCellstatement and proof · cited by 75
Topology.RelCWComplex.closedCellstatement and proof · cited by 70
Set.image_unionproof · cited by 48

Cited by4

Results whose statement or proof uses this declaration.

Topology.RelCWComplex.isClosed_of_isClosed_inter_openCell_or_isClosed_inter_closedCellproof · cited by 2
Topology.RelCWComplex.skeletonLT_inter_closedCell_eq_skeletonLT_inter_cellFrontierproof · cited by 2
Topology.RelCWComplex.cellFrontier_subset_finite_openCellproof · cited by 1
Topology.CWComplex.cellFrontier_union_openCell_eq_closedCellproof · cited by 0