Let $\beta X$ be the Stone-Čech compactification and $\upsilon X$ be the Hewitt real compactification of a completely regular space $X$.

It is well known that any continuous surjective map $f:X\rightarrow Y$ induces surjective map $\beta \left( f\right) :\beta X\rightarrow \beta Y$. Similarly, Is the induced map $\upsilon \left( f\right) :\upsilon X\rightarrow \upsilon Y$ surjective?