rs
| we began with the family !B! of open intervals, and from this
| family constructed the topology !T!.  The same method is useful
| in other situations and we now examine the construction in detail.
|
| A family !B! of sets is a 'base for a topology' !T!
| iff !B! is a subfamily of !T! and for each point x
| of the space, and each neighborhood U of x, there
| is a member V of !B! such that x in V c U.
|
| Thus the family of open intervals is a base for the usual topology of
| the real numbers, in view of