A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the subsets.
A subbasis for the Euclidean topology of the real line is formed by all intervals 
and 
: in fact a basis is formed by the open intervals
.
A subbasis for the discrete topology of the real line is formed by all subsets of 
having a given number 
of elements, since every singleton set 
can be obtained as the intersection of the sets 
and 
.
A subbasis for the Zariski topology of the affine space 
is formed by the complement sets of all irreducible affine
varieties. This follows applying de Morgan's laws
when considering that the open sets are the complement sets of the affine
varieties, and each of these is the union of a finite number of irreducible varieties.
