Theorems · Theorem · general topology
Convexity.continuous_convexCombPair
∀ {X : Type u_2} [inst : Convexity.ConvexSpace ℝ X] [inst_1 : MetricSpace X] [Convexity.IsConvexDist X],
Continuous fun x => Convexity.convexCombPair (↑x.1) (1 - ↑x.1) ⋯ ⋯ ⋯ x.2.1 x.2.2The convex combination (t, p, q) ↦ t • p + (1 - t) • q is continuous on [0, 1] × X × X
for a convex metric space X.
- Defined in
- Mathlib.Analysis.Convex.MetricSpace
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Set.Iccstatement and proof · cited by 1,702
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
Cited by2
Results whose statement or proof uses this declaration.
- Convexity.continuous_convexCombPair_of_isBoundedproof · cited by 1
- Convexity.continuous_convexComboPairproof · cited by 0