MathGloss

A topological space XX is simply connected if it is path-connected and for every two continuous maps γ1:[0,1]X\gamma_1:[0,1]\to X and γ2:[0,1]X\gamma_2:[0,1]\to X there exists a homotopy F:[0,1]×[0,1]XF:[0,1]\times[0,1]\to X such that F(x,0)=γ1(x)F(x,0)= \gamma_1(x) and F(x,1)=γ2(x)F(x,1) = \gamma_2(x).

A topological space XX is simply connected if it is path-connected and has trivial fundamental group.

Wikidata ID: Q912058