ions of
| members is a local base.  If U_1, U_2, ..., U_n, ... is a countable local subbase,
| then V_1, V_2, ..., V_n, ... where V_n = |^|{U_k : k =&lt; n} is a countable local base.
| Hence the existence of a countable local subbase at each point implies the first axiom
| of countability.
|
| JLK, Gen Top, page 50.
|
| John L. Kelley, 'General Topology',
| Van Nostrand Reinhold, New York, NY, 1955.

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