Subbasis of a topology
= Subbasis of a topology
{title2=$\mathcal S$}
A family of open subsets is a <subbasis of a topology> when its finite intersections form a <basis of a topology>, including the empty <intersection> equal to the entire space. For the <product topology>, <inverse images> of <open sets> under the <product projections> form the standard <subbasis of a topology>. A map into the space is continuous if the <inverse image> of every subbasic set is open.