Definition: Let X and Y be topological spaces. A function h: X → Y is said to be a homeomorphism if and only if the following conditions are satisfied:

• the function h: X → Y is both injective and surjective (so that the function h: X → Y has a well-defined inverse h⁻¹: Y → X),

• the function h: X → Y and its inverse h⁻¹: Y → X are both continuous.

Two topological spaces X and Y are said to be homeomorphic if there exists a homeomorphism h: X → Y from X to Y .