Suppose U is open in R2 and f:U⊆R2→R is continuous. The graph of f over U is the set S={(x,y,z):z=f(x,y),(x,y)∈U}. Prove that F:U⊆R2→R3, defined by F(u,v)=(u,v,f(u,v)), restricts to F:U→S and the restriction is a homeomorphism from U to S. This shows that the open set U and the graph S are "continuously similar shapes."