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Theorems · Theorem · functional analysis

interior_sphere

∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [NormedSpace ℝ E] (x : E) {r : ℝ},
  r ≠ 0 → interior (Metric.sphere x r) = ∅
Defined in
Mathlib.Analysis.Normed.Module.RCLike.Real
Cited by
1 results in Mathlib
Foundations
Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroupNormedSpace
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Around this declaration

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

frontier_sphere · cited by 0frontier_sphereSet · cited by 53352SetReal · cited by 25697RealNormedSpace · cited by 12499NormedSpaceSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupinterior · cited by 714interiorMetric.sphere · cited by 371Metric.sphereMetric.isClosed_closedBall · cited by 28Metric.isClosed_closedBallfrontier_closedBall · cited by 4frontier_closedBallinterior_frontier · cited by 3interior_frontierinterior_sphereCITED BYCITES

Cites9

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Cited by1

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