Topology is a major area of mathematics concerned with the properties of geometric objects that are preserved under continuous deformations, such as stretching, bending, and twisting, but not tearing or gluing. Often called "rubber sheet geometry," this field ignores rigid metric properties like distance and angles to focus instead on qualitative attributes like connectivity, compactness, and, most famously, the number of holes in an object. For this reason, a coffee mug is topologically equivalent to a donut (a torus), as both possess a single hole, an invariant property that allows one to be smoothly reshaped into the other.