Topological shapes refer to the properties of geometric figures that remain unchanged even when the shapes are stretched, twisted, or deformed, as long as they are not torn or glued. This branch of mathematics, known as topology, studies these properties to understand how different shapes relate to one another. Common examples of topological shapes include a torus, which resembles a doughnut, and a sphere, like a basketball. In topology, a torus and a sphere are considered different because one has a hole while the other does not. This focus on connectivity and continuity is essential in various fields, including physics and computer science.