Theorems · Theorem · algebraic topology
simply_connected_def
Deprecated since 2026-01-08Use simplyConnectedSpace_iff instead.
∀ (X : Type u_3) [inst : TopologicalSpace X], SimplyConnectedSpace X ↔ Nonempty (FundamentalGroupoid X ≌ CategoryTheory.Discrete Unit)
Alias of simplyConnectedSpace_iff.
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- 0 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Equivalencestatement · cited by 601
- FundamentalGroupoidstatement · cited by 60
- SimplyConnectedSpacestatement · cited by 19
- simplyConnectedSpace_iffproof · cited by 1
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