1. In topology, relating to or denoting a continuous deformation between two spaces that preserves their topological properties without tearing or gluing.
Usage: mathematics; technical

Examples

• A coffee cup and a donut are homeomorphic because one can be continuously deformed into the other.
• In topology, a sphere and a cube are homeomorphic shapes.
• Two spaces are homeomorphic if there exists a continuous bijection between them with a continuous inverse.
• The mathematician proved that the two manifolds were homeomorphic by constructing an explicit homeomorphism.
• Homeomorphic spaces share the same topological properties, such as connectedness and compactness.