Let  be a topological space, then is said to be second countable space, if  has a countable bases.
            In other words, a topological space  is said to be second countable space if it has a countable open base. A second countable space is also said to be a space satisfying the second axiom of countability.

Example:
            If is finite, then member of each on is finite. So its base is finite. Hence  is second countable space. Now we show that  is first countable. Let  is subbase of . So,  (Countable), then  (countable),  so is also countable.
            Therefore,  is second countable space, as each local base is also countable, so this is also first countable space.

Theorems:

• Every second countable space is first countable space, but the converse may not be true.
• Any uncountable set with co-finite topology is not first countable and so is not second countable.
• The set of all intervals with rational ends is a countable base for the usual topology on . The real line is second countable space.
• Any uncountable set  with countable topology is not first countable and so is not second countable.