Hi,

Could someone help me prove the following:

Let $\displaystyle f:X \to Y$ be a continuos map between metric-spaces $\displaystyle (X,d_{X})$ and $\displaystyle (Y,d_{Y})$. Prove that if $\displaystyle T \subseteq X$ is a pathwise connected subset in $\displaystyle X$, then the image $\displaystyle f(T) \subseteq Y$ under $\displaystyle f$ is a pathwise connected subset in $\displaystyle Y$.