Theorems · Definition · algebraic topology
IsSimplyConnected
{X : Type u_1} → [TopologicalSpace X] → Set X → PropWe say that a set is simply connected if it's a simply connected topological space in the induced topology.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- SimplyConnectedSpaceproof · cited by 19
Cited by13
Results whose statement or proof uses this declaration.
- Homeomorph.isSimplyConnected_imagestatement · cited by 3
- IsSimplyConnected.simplyConnectedSpacestatement and proof · cited by 2
- isSimplyConnected_smul_set_iffstatement · cited by 1
- Topology.IsEmbedding.isSimplyConnected_imagestatement · cited by 1
- IsSimplyConnected.isPathConnectedstatement and proof · cited by 1
- IsSimplyConnected.nonemptystatement and proof · cited by 1
- Complex.exists_continuousOn_eqOn_exp_compstatement and proof · cited by 1
- Complex.exists_continuousOn_pow_eqstatement and proof · cited by 1
- Complex.UnitDisc.exists_continuousOn_pow_eqstatement and proof · cited by 0
- isSimplyConnected_iff_exists_homotopy_refl_forall_memstatement · cited by 0
- isSimplyConnected_smul_set₀_iffstatement · cited by 0
- isSimplyConnected_vadd_set_iffstatement · cited by 0