A topological property is a characteristic of a geometric object that remains unchanged under continuous deformations, such as stretching or bending, but not tearing or gluing. Examples of topological properties include the number of holes in an object or its connectedness. These properties help classify shapes in the field of topology, a branch of mathematics. In topology, objects are often represented as topological spaces, which provide a framework for studying their properties. For instance, a torus and a coffee cup are considered equivalent in topology because they both have one hole, despite their different appearances.