Background
A CW complex is a Hausdorff space and it is the union of its some of its subsets called cells, and cells are homeomorphic images in $X$ of some closed $k$-balls.
The weak topology of a CW complex X is defined as the topology having the property that a subset of $X$ is closed if and only if it is closed in each cell of $X$.
The question
What is the motivation of requiring that the topology is weak? What is, if $X$ has more closed sets then in this definition, and what is if it has less. And why are closed sets are generally used in this definition, why not open sets? (I saw in some places this definition with open sets. Is it an error, or it is an equivalent definition?)