Theorems · Theorem · algebraic topology
Topology.CWComplex.Subcomplex.union_closedCell
∀ {X : Type u_1} [t : TopologicalSpace X] {C : Set X} [T2Space X] [inst : Topology.CWComplex C]
(E : Topology.RelCWComplex.Subcomplex C), ⋃ n, ⋃ j, Topology.RelCWComplex.closedCell n ↑j = ↑EA subcomplex is the union of its closed cells.
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- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- SetLike.coestatement · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Set.iUnionstatement and proof · cited by 2,483
- T2Spacestatement and proof · cited by 1,351
- Topology.RelCWComplex.cellstatement · cited by 194
- Topology.RelCWComplex.Subcomplexstatement and proof · cited by 110
- Topology.RelCWComplex.closedCellstatement and proof · cited by 70
- Set.empty_unionproof · cited by 52
- Topology.CWComplexstatement and proof · cited by 44
- Topology.RelCWComplex.Subcomplex.Istatement and proof · cited by 32
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