fies the 'first axiom of countability' if the neighborhood
| system of every point has a countable base.  It is clear that each topological space
| which satisfies the second axiom of countability also satisfies the first;  on the
| other hand, any uncountable discrete topological space satifies the first axiom
| (there is a base for the neighborhood system of each point x which consists
| of the single neighborhood {x}) but not the second (the cover whose members
| are {x} for all x in X has no countable s