coverings

In topology, a covering (or covering space) is a way of representing a complex shape using simpler, overlapping parts. Imagine a shape like a sphere or a doughnut (torus). A covering space is a new space that "wraps around" the original shape multiple times, with each point in the original being "covered" by one or more points in the covering space. This helps mathematicians study complicated surfaces by analyzing these simpler, layered structures, making it easier to understand their properties, such as connectivity and holes.