Mathlib Map

Theorems · Definition · algebraic topology

Topology.RelCWComplex.openCell

{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 open n-cell given by the index i. Use this instead of map n i '' ball 0 1 whenever possible.

Defined in
Mathlib.Topology.CWComplex.Classical.Basic
Cited by
75 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.RelCWComplex.openCell_subset_closedCell · cited by 8RelCWComplex.openCell_sub…Topology.RelCWComplex.disjoint_openCell_of_ne · cited by 6RelCWComplex.disjoint_ope…Topology.RelCWComplex.cellFrontier_union_openCell_eq_closedCell · cited by 4RelCWComplex.cellFrontier…Topology.RelCWComplex.Subcomplex.closedCell_subset_of_mem · cited by 4Subcomplex.closedCell_sub…Topology.RelCWComplex.disjointBase · cited by 4RelCWComplex.disjointBaseTopology.RelCWComplex.disjoint_skeletonLT_openCell · cited by 4RelCWComplex.disjoint_ske…Topology.RelCWComplex.closure_openCell_eq_closedCell · cited by 3RelCWComplex.closure_open…Topology.RelCWComplex.Subcomplex.union · cited by 3Subcomplex.unionTopology.RelCWComplex.Subcomplex.subset_complex · cited by 3Subcomplex.subset_complexTopology.RelCWComplex.map_zero_mem_openCell · cited by 3RelCWComplex.map_zero_mem…Topology.RelCWComplex.openCell_zero_eq_singleton · cited by 3RelCWComplex.openCell_zer…Topology.RelCWComplex.skeletonLT_inter_closedCell_eq_skeletonLT_inter_cellFrontier · cited by 2RelCWComplex.skeletonLT_i…Topology.CWComplex.Subcomplex.mk' · cited by 2Subcomplex.mk'Topology.CWComplex.Subcomplex.mk'' · cited by 2Subcomplex.mk''Topology.RelCWComplex.Subcomplex.mk' · cited by 2Subcomplex.mk'Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.image · cited by 5609Set.imagePartialEquiv.toFun · cited by 821PartialEquiv.toFunMetric.ball · cited by 735Metric.ballTopology.RelCWComplex · cited by 195Topology.RelCWComplexTopology.RelCWComplex.cell · cited by 194RelCWComplex.cellTopology.RelCWComplex.map · cited by 44RelCWComplex.mapRelCWComplex.openCellCITED BYCITES

Cites8

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Cited by84

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