In
mathematics, a
base (or
basis)
B for a
topological space X with
topology T is a collection of
open sets in
T such that every open set in
T can be written as a union of elements of
B. We say that the base
generates the topology
T. Bases are useful because many properties of topologies can be reduced to statements about a base generating that topology, and because many topologies are most easily defined in terms of a base which generates them.