"show that in a discrete metric space, singleton sets are the only nonempty connected sets"
i have no idea how to go about this one =/
A discrete metric space gives rise to the discrete topology. So, let $\displaystyle M$ be the metric space in common. Clearly each singleton is connected. But, given any $\displaystyle m,m'\in M$ clearly $\displaystyle \{m\}\cup\{m'\}=\{m,m'\}$ is a separation of $\displaystyle \{m,m'\}$ since each $\displaystyle \{m\},\{m'\}\subseteq M$ are open.