Homeomorphisms

A homeomorphism is a concept in mathematics, particularly in topology, that describes a special kind of relationship between two shapes or spaces. Two spaces are homeomorphic if one can be transformed into the other without tearing or gluing, just stretching or bending. This means they have the same essential shape or structure, even if they look different. For example, a coffee cup and a donut are homeomorphic because you can deform one into the other. In essence, homeomorphisms help us understand the intrinsic properties of shapes that remain unchanged under continuous transformations.