TopOlogy

Topology is a branch of mathematics dealing exclusively with properties of continuity.  Formally, a topology for a space X is defined a set T of subsets of X satisfying:

1) T is closed under abitrary unions
2) T is closed under finite intersections
3) X, {} are in T

The sets in T are referred to as open sets, and their complements as closed sets.  Roughly speaking open sets are thought of as neighborhoods of points.  This definition of topology is too general to be of much use and so normally additional conditions are imposed.