Name for equivalent mapping from a function in $\mathbb{R}$ to $\mathbb{R}^2$

Question

Suppose there could be a function $f: \mathbb{R} \rightarrow \mathbb{R}$, for instance $f(x) = x^2$, and an equivalent set of points in $\mathbb{R}^2$ that represent the same $(x,y)$ points as this function. Is there some sort of name for this equivalency, or mapping, between two identical sets within two different spaces like this? I'm thinking something along the lines of Homomorphism? or maybe some term within Topology?

Answer 1

Given a function $f: \mathbb{R}^n \rightarrow \mathbb{R}$, one constructs the graph of $f$ in $\mathbb{R}^{n+1}$ as $\{(x,y){ }|{ } y=f(x) \}$. If $f$ is continuous, then the domain $\mathbb{R}^n$ is homeomorphic to the graph of $f$. See a proof here: Is the graph of a continuous function homeomorphic to its domain?