Question 145
Let $f:[0,1] \rightarrow[0,1]$ be a function with the property that for every $y \in[0,1]$ and every $\varepsilon \gt 0$ there exists $x \in[0,1]$ such 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 property in the statement 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 property in the statement which is not surjective.