What is the difference between a base and a subbase?

Question

Is the base the one that generates the topology? If so, then what is the subbase?

Answer 1

A base for a topology T is a collection {U_a} of sets such that every set in T is the union of sets in {U_a}.

A subbase for a topology T is a collection {U_a} of sets such that every set in T can be written in terms of {U_a} using unions and finite intersections.

If you start with a collection of sets {U_a} and consider the smallest topology T containing this collection, then {U_a} will be a subbase for T.