n !B! such that x in W c U, and consequently
| x in V.  Hence U c V and since V is surely a subset of U, we have that V = U.
| To show the converse, suppose !B! c !T! and each member of !T! is the union
| of members of !B!.  If U in !T!, then U is the union of the members of
| a subfamily of !B!, and for each x in U there is V in !B! such that
| x in V c U.  Consequently !B! is a base for !T!.
|
| Although this is a very convenient method for the construction
| of topologies, a little caution is necessary b