Open vs Closed Sets for studying topology Topologies can be defined either in terms of the closed sets or the open sets.  Yet most proofs, examples, problems, etc. in standard texts concern the open sets.  
I would think closed sets are easier and more intuitive for most people. So, is there a particular reason it is better to work primarily with the open sets?
 A: I don't have a good answer for your question, but would just like to reproduce a quote from the book I'm studying topology from (Simmons, see my user page).  On page 98, Simmons writes

The last two theorems show that it is possible to approach the subject of topological spaces by taking either closed sets or a closure operation as the basic undefined concept. A good deal of research was done along these lines in the early days of topology. It was found that there are many different ways of defining a topological space, all of which are equivalent to one another. Several decades of experience have convinced most mathematicians that the open set approach is the simplest, the smoothest and the most natural

However I don't know any more than this, so apologies for posting this as an answer (it is too long for a comment).
A: Perhaps the reason is that many proofs and definitios rely on open neighbourhoods. I think that an open set that contains a point is more intuitive that a closed set that doesn't.
Take, for example, this definition of limit:
$\lim_{x\to a}f(x)=L$ if for every $\epsilon>0$ there exists some $\delta>0$ such that $|a-x|\ge\delta$ or $a=x$ whenever $|f(x)-f(a)|\ge\epsilon$.
