“Smallest set” term in the trees set definition

Question

I often meet such kind of the definition of the set of trees, as:

The set of unranked $\Sigma$-trees, denoted by $T$, is the smallest set of strings over $\Sigma$ and the parenthesis symbols ‘)’ and ‘(’ such that for each $a\in\Sigma$ and $w\in T^*$, $a(w)$ is in $T$. (http://dl.acm.org/citation.cfm?id=2101368)

One question that I can not generally understand is: how does this definition prevent from the string, say "$a)($", appear in the set $T$?

Would somebody be so kind explain me this point?

And please, if you are going to downvote this question, be so kind explain why are you doing that.