👉 In mathematics and physics, a manifold is a topological space that locally resembles Euclidean space but has extra structure. These structures include differentiable functions on it, meaning that they can be integrated over to give a function from the underlying Euclidean space to itself. Manifolds are fundamental in many branches of science and engineering. In the context of physics, manifolds often refer to geometric spaces where physical quantities (such as forces or velocities) act locally according to certain rules. They are used
