Question 177
Let $f : [0, 1] \to [0, 1]$ be a function with the property that for every $y \in [0, 1]$ and every $\varepsilon \gt 0$ there exists $x \in [0, 1]$ so that $|f(x) - y| \lt \varepsilon$.
a) Prove that if $f$ is continuous on $[0, 1]$, then $f$ is surjective.
b) Give an example of a function $f$ with the given property which is not surjective.
a) Prove that if $f$ is continuous on $[0, 1]$, then $f$ is surjective.
b) Give an example of a function $f$ with the given property which is not surjective.