In technical terms, a homeomorphism is a bijective and continuous function between topological spaces that has a continuous inverse function. One of the most famous examples (and that actually comes in pretty handy for this) is our friend the quadratic function: f(x) = x^2. So, only real numbers can be used as inputs, and we can only get real numbers as outputs. In fact, try to think of any real number that when multiplied by itself, it gives a negative number. f: ℝ —> ℝ, f(x)=x is continuous, surjective AND injective — so it is also bijective!