In topology and in calculus, a round function is a scalar function Mto{mathbb{R}}, over a manifold M, whose critical points form one or several connected components, each homeomorphic to the circle S1, also called critical loops. They are special cases of Morse-Bott functions. Scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. Mathematically, a scalar field on a region U is a real or complex-valued function on U. The region U may be a set in some Euclidean space, or more generally a subset of a manifold, and it is typical to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order. In a mathematical context, the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form.

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