Property S

Let $(X,d)$ be a metric space and let $Y \subset X$ be nonempty. We say that $Y$ has property S if for each $\epsilon > 0$ there is a finite collection $\{A_1,\ldots,A_n\}$ of subsets of $Y$ each with diameter less than $\epsilon$ such that $Y = \displaystyle\bigcup_{i=1}^n A_i$.