Theorems · Theorem · general topology
Submodule.isPathConnected
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [ContinuousAdd E]
[ContinuousSMul ℝ E] (s : Submodule ℝ E), IsPathConnected ↑sA subspace in a topological vector space over ℝ is path connected.
- Defined in
- Mathlib.Analysis.Convex.PathConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- IsPathConnectedstatement · cited by 65
- Convex.isPathConnectedproof · cited by 8
- Submodule.convexproof · cited by 5
- Submodule.nonemptyproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- isPathConnected_compl_of_isPathConnected_compl_zeroproof · cited by 1