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differentiable

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So differentiable structures on a manifold is an example of topology. en.wikipedia.org

A function is (totally) differentiable if its total derivative exists at every point in its domain. en.wikipedia.org

Though the derivative of a differentiable function never has a jump discontinuity, it is possible for the derivative to have an essential discontinuity. en.wikipedia.org

In some sense a diffeology generalizes the concept of smooth charts in a differentiable manifold. en.wikipedia.org

For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly. en.wikipedia.org

Also, if "u" is differentiable in the conventional sense then its weak derivative is identical (in the sense given above) to its conventional (strong) derivative. en.wikipedia.org

It also has a standard differentiable structure on it, making it a differentiable manifold. en.wikipedia.org

First, it implies that a function which is holomorphic in an open set is in fact infinitely differentiable there. en.wikipedia.org

In geometry and topology, all manifolds are topological manifolds, possibly with additional structure, most often a differentiable structure. en.wikipedia.org

The property also means that every fundamental solution of an elliptic operator is infinitely differentiable in any neighborhood not containing 0. en.wikipedia.org

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