Connectedness

Simple connectedness

A path-connected space is simply connected¹ or 1-simply connected iff every continuous loop is null-homotopic, i.e. its fundamental group is trivial #m/def/homotopy

for any .

Examples

• Every Star domain is simply connected.
• Fundamental group of a sphere

Properties

• Simply connectedness Local simple connectedness Semilocal simple connectedness

#state/tidy | #lang/en | #SemBr