# Simply-connected topological space Intuitively, think of a space s.t., any closed curve on it can be retracted to a point. a counter example will be $\mathbb{R}^2-(0,0)$ i.e., the plain without the origin. any closed curve that contain the origin can't retract to a point. More exact, the closed curve in space $X$ can be classified by an equivalence relation where two curves are equivalent if one can continuously deformed to the other. The classes have group structure which is called the fundamental group and is written as $\pi_1(X)$. So a space is simply connected iff it has trivial fundamental group i.e., $\pi_1(X)=1$. ## Created 2026-06-03 16:47