Theorems · Theorem · algebraic topology
Topology.RelCWComplex.continuousOn
∀ {X : Type u} {inst : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (n : ℕ)
(i : Topology.RelCWComplex.cell C n), ContinuousOn (↑(Topology.RelCWComplex.map n i)) (Metric.closedBall 0 1)The characteristic maps are continuous when restricting to closedBall 0 1.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Topology.RelCWComplex
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousOnstatement · cited by 1,411
- PartialEquiv.toFunstatement · cited by 821
- Metric.closedBallstatement · cited by 704
- Topology.RelCWComplexstatement and proof · cited by 195
- Topology.RelCWComplex.cellstatement · cited by 194
- Topology.RelCWComplex.mapstatement · cited by 44
Cited by3
Results whose statement or proof uses this declaration.
- Topology.RelCWComplex.closure_openCell_eq_closedCellproof · cited by 3
- Topology.RelCWComplex.isCompact_cellFrontierproof · cited by 2
- Topology.RelCWComplex.isCompact_closedCellproof · cited by 2