Prove that $\displaystyle U \subset M$ is open if and only if whenever $\displaystyle (Xn)^\infty_{n=1}$ is a sequence of elements of M converging to some $\displaystyle x \in U$, then there exists $\displaystyle N \in N $, such that $\displaystyle Xn \in U $for every $\displaystyle n>=N$.

this is one of the question in my midterm test that i couldnt do, the prof is not giving out solution, need some help to prove this