Differential space

A differential space is a mathematical concept that generalizes the idea of smooth, curved surfaces or shapes. Think of it as a flexible framework that allows mathematicians to study various kinds of spaces, including more complex or irregular ones, using calculus-like tools. Unlike traditional smooth surfaces, a differential space can include structures with singularities or rough points, but still retains enough "smoothness" for analysis. This concept helps in understanding and working with spaces that are too complicated for standard geometry, providing a unified language to study their properties and behaviors mathematically.