Theorems · Theorem · geometry

AffineSubspace.isConnected_setOf_sSameSide

Deprecated since 2026-07-09Use AffineSubspace.isConnected_setOfPred_sSameSide instead.

∀ {V : Type u_2} {P : Type u_4} [inst : SeminormedAddCommGroup V] [inst_1 : NormedSpace ℝ V]
  [inst_2 : PseudoMetricSpace P] [inst_3 : NormedAddTorsor V P] {s : AffineSubspace ℝ P} {x : P},
  x ∉ s → (↑s).Nonempty → IsConnected {y | s.SSameSide x y}

Alias of AffineSubspace.isConnected_setOfPred_sSameSide.

Defined in

Mathlib.Analysis.Convex.Side

Cited by

0 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor