noun
- A continuous function between topological spaces that has a continuous inverse, establishing that two spaces have the same topological properties.
Usage: mathematics; topology
Examples
- A circle and an ellipse are homeomorphic because a homeomorphism can continuously deform one into the other.
- In topology, a homeomorphism preserves the essential structure of a space even if distances and angles change.
- The mathematician proved that the two surfaces were homeomorphic by constructing an explicit homeomorphism between them.
- Homeomorphism is a fundamental concept for classifying topological spaces.
- A coffee cup and a donut are homeomorphic in topology because each has exactly one hole.