Linked from

The 22 pages that link to Simply connected space, each with the reason it gives.

• Cauchy's integral formulaRelated: Simple connectivity is a common domain condition behind standard versions of the formula.

• Fundamental groupCompared with: Triviality marks the limit of what this invariant detects about loops.

• Riemann mapping theoremNarrower topic: Simple connectivity is the topological hypothesis that rules out holes in the domain.

• Residue theoremRelated: Domain topology helps determine whether contours enclose singularities or can be contracted away.

• Connected spaceBroader topic: Simple connectedness adds a condition on loops beyond the connectedness of the whole space.

• Conservative forceRelated: Zero curl guarantees a potential only with suitable domain conditions such as simple connectivity.

• Uniformization theoremRelated: Simple connectivity is the hypothesis that restricts the theorem to three models.

• Poincaré conjectureRelated: Simple connectivity is the conjecture’s topological condition distinguishing the sphere.

• Cauchy's integral theoremRelated: Simple connectivity lets the theorem apply to every closed contour in the domain.

• Grigori PerelmanRelated: Simple connectivity is the hypothesis that distinguishes the manifolds in the conjecture.

• Magnetic vector potentialRelated: Topology affects whether a global potential exists and whether it is unique up to gauge.

• Rouché's theoremRelated: Simple connectivity often helps establish the domains used in applications of the theorem.

• Alexander horned sphereCompared with: The sphere’s complement fails precisely this property.

• Conservative vector fieldRelated: On such suitable domains, zero curl implies conservativeness.

• Lie's third theoremRelated: Simple connectivity selects the global integration without nontrivial covering ambiguity.

• Nonconservative forceRelated: The domain's topology matters when inferring path independence from zero curl.

• Solenoidal vector fieldRelated: Topology affects whether a divergence-free field admits a global vector potential.

• Bendixson–Dulac theoremRelated: Simple connectivity ensures a closed planar orbit encloses a region without a hole.

• Gradient theoremRelated: This topological condition helps ensure that curl-free fields have global potentials.

• Morera's theoremRelated: Simple connectivity helps extend triangle-integral cancellation to integrals along broader closed paths.

• Seifert–Van Kampen theoremRelated: Trivial groups in pieces or intersections can simplify the theorem's pushout.

• Brennan conjectureRelated: The conjecture's target domains have no topological holes.