Collection of subsets that generate a topology
This article is about an object in mathematical topology. For the term in highway engineering, see
Subbase (pavement). For the frequency range, see
Sub-bass.
In topology, a subbase (or subbasis, prebase, prebasis) for a topological space
with topology
is a subcollection
of
that generates
in the sense that
is the smallest topology containing
as open sets. A slightly different definition is used by some authors, and there are other useful equivalent formulations of the definition; these are discussed below.