Let $I$ be closed n-dimensional intervals, $$I=\{\mathbf{x}: a_j\le x_j \le b_j, \quad j=1, \cdots, n\}$$
and $S$ be a countable collection of intervals $I_k$, $$S=\{I_j,\quad j=1, 2, \cdots\}$$
In this case, if $\displaystyle E\subset\cup_{I_j\in S}I_j$, $S$ is a _____ of $E$.
covering or cover?
My professor said us covering, but wikipedia said us cover. Which is correct?