Extension theorems address the fundamental problem of when and how a function defined on a subset of a metric space can be extended to the whole space without loss of regularity. Originating in the ...

👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

The generalized Cantor function Ѳϒ has a derivative equal to 1/(1 — γ) at almost every point in the set Cγ. This was established by Darst [1] who then posed the problem of characterizing those points ...