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Let $X,Y$ be topological spaces, and $a$ a net in $X$. Let $f:X\to Y$ and $g:Y\to X$ be two functions.

Choose the correct statements below. Select ALL that apply.

$g(a)$ is a net in $X\!$.

$f(a)$ is a net in $Y\!$.

$g(f(a))$ is a net in $X\!$.

$g(f(a))$ is a net in $Y\!$.

$f(g(a))$ is a net in $Y\!$.