Sheaf (mathematics) and Smoothness

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Difference between Sheaf (mathematics) and Smoothness

Sheaf (mathematics) vs. Smoothness

In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

Analytic continuation

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

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Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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Real line

In mathematics, the real line, or real number line is the line whose points are the real numbers.

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Sheaf (mathematics)

In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.

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Support (mathematics)

In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

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