Round function

In topology and in calculus, a round function is a scalar function M → R {displaystyle M o {mathbb {R} }} , over a manifold M {displaystyle M} , whose critical points form one or several connected components, each homeomorphic to the circle S 1 {displaystyle S^{1}} , also called critical loops. They are special cases of Morse-Bott functions. In topology and in calculus, a round function is a scalar function M → R {displaystyle M o {mathbb {R} }} , over a manifold M {displaystyle M} , whose critical points form one or several connected components, each homeomorphic to the circle S 1 {displaystyle S^{1}} , also called critical loops. They are special cases of Morse-Bott functions. For example, let M {displaystyle M} be the torus. Let