Continuity of finite intersection of continuous correspondence

Question

I was solving a problem which requires me to show the continuity of a set-valued map. Suppose $\Bigl(T(x_i)\Bigr)_{i=1}^{n} \subset A$, where the set-valued map $T$ defined as $\mathbb{X} \ni x \mapsto T(x) \subset A$. Moreover, we know that for each $i=1,\cdots,n$; $T(x_i)$ is continuous over its domain. Is there any result that asserts that the finite intersection $\cap_{i=1}^n T(x_i)$ is also continuous?