👉 A manifold is an abstract mathematical concept used to describe spaces that are locally similar but not identical. These spaces can be thought of as sets or topological spaces where certain properties such as continuity, differentiability, and uniqueness are preserved under continuous deformations. Manifolds are fundamental in mathematics and physics for their ability to capture the behavior of many physical systems, including those involving smooth curves like a sphere or surfaces that curve smoothly around other surfaces. They also have many applications in engineering, particularly in the
