Theorems · Theorem · algebraic topology
Topology.CWComplex.continuousOn
∀ {X : Type u} {inst : TopologicalSpace X} {C : Set X} [self : Topology.CWComplex C] (n : ℕ)
(i : Topology.CWComplex.cell C n), ContinuousOn (↑(Topology.CWComplex.map n i)) (Metric.closedBall 0 1)The characteristic maps are continuous when restricting to closedBall 0 1.
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- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Topology.CWComplex
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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
- 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.CWComplexstatement and proof · cited by 44
- Topology.CWComplex.cellstatement · cited by 13
- Topology.CWComplex.mapstatement · cited by 12
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