In mathematics, particularly in topology, two shapes are considered homeomorphic if they can be transformed into each other through continuous stretching or bending, without tearing or gluing. This means that they share the same fundamental properties, such as the number of holes or connected components, even if their appearances differ. For example, a coffee cup and a donut are homeomorphic because each has one hole. You can imagine deforming the coffee cup into a donut shape by stretching the handle into a circular form. This concept helps mathematicians understand the intrinsic properties of shapes beyond their visual characteristics.