Subbasis for a topological space

Definition
A subbasis for a topological space is a collection of open subsets of the topological space such that the following equivalent conditions hold:


 * The set of subsets obtained by taking finite (possibly empty) intersections of these, form a basis for the topological space
 * Every open subset is a countable union of finite intersections of these
 * The topology on the space is the coarsest topology for which the given subsets are all open

No constraints are there for a collection of subsets to form a subbasis.

Related notions

 * Basis for a topological space