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Theorems · Definition · algebraic topology

Topology.RelCWComplex.cellFrontier

{X : Type u_1} →
  [t : TopologicalSpace X] →
    {C D : Set X} → [inst : Topology.RelCWComplex C D] → (n : ℕ) → Topology.RelCWComplex.cell C n → Set X

The boundary of the n-cell given by the index i. Use this instead of map n i '' sphere 0 1 whenever possible.

Defined in
Mathlib.Topology.CWComplex.Classical.Basic
Cited by
45 results in Mathlib
Foundations
Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopology.RelCWComplex

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Topology.CWComplex.OneSkeletonGraph · cited by 8CWComplex.OneSkeletonGraphTopology.RelCWComplex.cellFrontier_subset_closedCell · cited by 4RelCWComplex.cellFrontier…Topology.RelCWComplex.cellFrontier_union_openCell_eq_closedCell · cited by 4RelCWComplex.cellFrontier…Topology.RelCWComplex.cellFrontier_subset_base_union_finite_closedCell · cited by 3RelCWComplex.cellFrontier…Topology.RelCWComplex.cellFrontier_subset_skeletonLT · cited by 3RelCWComplex.cellFrontier…Topology.RelCWComplex.skeletonLT_inter_closedCell_eq_skeletonLT_inter_cellFrontier · cited by 2RelCWComplex.skeletonLT_i…Topology.RelCWComplex.cellFrontier_one_eq · cited by 2RelCWComplex.cellFrontier…Topology.RelCWComplex.cellFrontier_zero_eq_empty · cited by 2RelCWComplex.cellFrontier…Topology.RelCWComplex.iUnion_cellFrontier_subset_skeletonLT · cited by 2RelCWComplex.iUnion_cellF…Topology.RelCWComplex.isClosed_cellFrontier · cited by 2RelCWComplex.isClosed_cel…Topology.RelCWComplex.isClosed_inter_cellFrontier_succ_of_le_isClosed_inter_closedCell · cited by 2RelCWComplex.isClosed_int…Topology.RelCWComplex.isClosed_of_isClosed_inter_openCell_or_isClosed_inter_closedCell · cited by 2RelCWComplex.isClosed_of_…Topology.RelCWComplex.isCompact_cellFrontier · cited by 2RelCWComplex.isCompact_ce…Topology.CWComplex.exists_cellFrontier_one_eq · cited by 1CWComplex.exists_cellFron…Topology.RelCWComplex.skeleton_inter_closedCell_eq_skeleton_inter_cellFrontier · cited by 1RelCWComplex.skeleton_int…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.image · cited by 5609Set.imagePartialEquiv.toFun · cited by 821PartialEquiv.toFunMetric.sphere · cited by 371Metric.sphereTopology.RelCWComplex · cited by 195Topology.RelCWComplexTopology.RelCWComplex.cell · cited by 194RelCWComplex.cellTopology.RelCWComplex.map · cited by 44RelCWComplex.mapRelCWComplex.cellFrontierCITED BYCITES

Cites8

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Cited by46

Results whose statement or proof uses this declaration.