I am having trouble understanding topology. I have read the sections 3 times and hasn't helped.

Could someone explain this question, the methodology to answering it, and how it is done?

Let X be a topological space; let A be a subset of X. Suppose that for each $\displaystyle x\in A$ there is an open set U containing x such that $\displaystyle U\subset A$. Show A is open in X.