Base for a topology

context	$\langle X,T\rangle$ … topological space
definiendum	$B\in$ it
inclusion	$B\subseteq T$
for all	$U\in T$
exists	$C\subseteq B$
postulate	$U=\bigcup C$

A base $B$ for a topology is a collection its open sets, which suffice to cover any open set.