👉 In mathematics, a manifold is an abstract space that can be thought of as a geometric object that has properties that are invariant under continuous deformations. Manifolds have a fundamental property known as "topological invariance," which means that they preserve certain topological structures such as connectedness and smoothness. Manifolds are ubiquitous in various fields, including geometry, topology, and physics. They can be used to describe the properties of mathematical objects like curves, surfaces, manifolds,