homeomorphism

A homeomorphism is a way of showing that two shapes are fundamentally the same in terms of their structure, even if they look different. Imagine stretching or bending a rubber sheet without tearing or gluing it; the shape remains connected and continuous. If you can deform one shape into another through such a continuous process without cutting or gluing, they are called homeomorphic. This concept helps mathematicians identify when two objects are equivalent in their topological properties, meaning their core form remains unchanged despite transformations like stretching or bending.