Definition of topology I am learning the topology from the book by Munkres. Munkres starts up the topic by describing the way topology was defined. It says that whensoever we define anything in mathematics we define it in such a way that it covers some interesting aspects of mathematics that can be studied under that object being defined and at the same time it should be restricted from being over general. 
Can anyone shed some light on the way the definition of topology was formulated along the lines aforementioned?
May I know the difference between point set topology and general topology?
 A: A Topology comes from the set of neighborhoods of points. When you're doing calculus (infinitesimal calculus - derivatives and limits of functions), say, looking at a limit of a function at a point. You're looking at what happens to value of the function when you're delving closer and closer to a given point - that is, you're looking at the relation between the set of values of the function and the set of neighborhoods of the point. All of calculus is built on such considerations. By studying topology, you can redefine problems in calculus in a way that makes them much more simple, and topology then allows you to try and do similar things on spaces which are less convenient than the Euclidean Spaces.
An example - think about the definition of an equi-continuous function. The $\delta-\epsilon$ definition is annoying. When you define it in terms of small open sets, rather then epsilons and deltas, the outcome is a beautiful and revealing definition which actually tells you something intuitive about the function.
