Theorems · Theorem · general topology
Convex.isPreconnected
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [ContinuousAdd E]
[ContinuousSMul ℝ E] {s : Set E}, Convex ℝ s → IsPreconnected sA convex set is preconnected.
- Defined in
- Mathlib.Analysis.Convex.PathConnected
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.Nonemptyproof · cited by 2,627
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- Convexstatement and proof · cited by 551
- Set.eq_empty_or_nonemptyproof · cited by 248
- IsPreconnectedstatement · cited by 205
- IsConnected.isPreconnectedproof · cited by 36
Cited by14
Results whose statement or proof uses this declaration.
- hasFDerivAt_jacobiTheta₂proof · cited by 4
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2
- integral_gaussian_complexproof · cited by 2
- AnalyticAt.eventually_constant_or_nhds_le_map_nhdsproof · cited by 1
- Sion.exists_lt_iInf_of_lt_iInf_of_supproof · cited by 1
- Metric.isPreconnected_closedBallproof · cited by 1
- DiffContOnCl.ball_subset_image_closedBallproof · cited by 1
- Metric.isPreconnected_closedEBallproof · cited by 1
- ProbabilityTheory.eqOn_complexMGF_of_mgf'proof · cited by 1
- QuasiconcaveOn.isPreconnected_preimage_subtypeproof · cited by 1
- Complex.eq_const_of_exists_maxproof · cited by 1