Theorems · Theorem · convex and discrete geometry
QuasilinearOn.isPreconnected_preimage_subtype
∀ {E : Type u_4} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [IsTopologicalAddGroup E]
[ContinuousSMul ℝ E] {β : Type u_5} [inst_5 : Preorder β] {f : E → β} {s : Set E} {t : β},
QuasilinearOn ℝ s f → IsPreconnected (Subtype.val ⁻¹' f ⁻¹' Set.Iic t)- Defined in
- Mathlib.Analysis.Convex.Quasiconvex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Preorderstatement and proof · cited by 7,952
- Set.Elemstatement · cited by 7,166
- Set.preimagestatement · cited by 4,946
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- Set.Iicstatement · cited by 1,111
- ContinuousSMulstatement and proof · cited by 1,016
- IsPreconnectedstatement · cited by 205
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