Theorems · Theorem · functional analysis
isConnected_setOfPred_sameRay
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (x : E), IsConnected {y | SameRay ℝ x y}The set of vectors in the same ray as x is connected.
- Defined in
- Mathlib.Analysis.Normed.Module.Convex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Moduleproof · cited by 20,661
- NormedSpacestatement and proof · cited by 12,499
- LinearOrderproof · cited by 8,572
- Fieldproof · cited by 7,404
- Set.ofPredstatement and proof · cited by 6,101
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- IsStrictOrderedRingproof · cited by 2,490
- Set.Iciproof · cited by 1,070
- SameRaystatement · cited by 149
- IsConnectedstatement and proof · cited by 116
- continuousOn_id'proof · cited by 109
Cited by1
Results whose statement or proof uses this declaration.
- isConnected_setOf_sameRayproof · cited by 0