Let $(M,d)$ be a metric space. Then $ x \in S $ is an interior point of $ S $ if some ball centered around S of positive radius is wholly contained in $S$.
But consider this. The set $S_{L}$ of all strings of length $L$ is a metric space under the Hamming distance. Let $S \subset S_{L}$ and Let $s \in S$ be any string in $S$. Then technically, the ball of radius 0.5 centered on $s$ must be be wholly contained in $S$ since this ball can contain no string other than $s$ itself. Therefore, $s$ is an interior point of $S$, therefore $S$ is open. Does this mean that every subset of $S_{L}$ is necessarily open, or is there some major flaw that I have missed in the definition of an interior point(which I am quite sure I have)?