Open subset

Definition
A subset of a topological space is termed open if it satisfies the following equivalent conditions:


 * In terms of the standard definition of topology in terms of open subsets: It is one of the member of the topology
 * In terms of a basis: It is a union (possibly empty) of basis open sets
 * In terms of a subbasis: It is a union (possibly empty) of finite intersections of subbasis open sets
 * In terms of closed subsets: It is the set-theoretic complement of a closed subset