I don't know what this double-arrow $\twoheadrightarrow$ means!
From Wikipedia: Surjective funtion
A surjective function is a function whose image is equal to its codomain. Equivalently, a function f with domain $X$ and codomain $Y$ is surjective if for every $y$ in $Y$ there exists at least one $x$ in $X$ with $f(x)=y$. Surjections are sometimes denoted by a two-headed rightwards arrow, as in $f : X \twoheadrightarrow Y,\;$ [Boldface mine.]
See also the section on the properties or characterizations of "surjections".