A homeomorphism is a concept in topology that describes a special type of mapping between two spaces. Specifically, it is a continuous function that has a continuous inverse, meaning that both the function and its reverse do not break or tear the spaces involved. If two spaces can be transformed into each other through a homeomorphism, they are considered topologically equivalent, even if their shapes differ. In simpler terms, think of a homeomorphism as a way to stretch or bend an object without cutting or gluing. For example, a coffee cup and a donut are homeomorphic because one can be transformed into the other without any breaks, demonstrating that they share the same topological properties.