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Countably generated space
In mathematics, a topological space ''X'' is called countably generated if the topology of ''X'' is determined by the countable sets in a similar way as the topology of a sequential space (or a Fréchet space) by the convergent sequences.
The countable generated spaces are precisely the spaces having countable tightness - therefore the name ''countably tight'' is used as well.
==Definition==
A topological space ''X'' is called countably generated if ''V'' is closed in ''X'' whenever for each countable subspace ''U'' of ''X'' the set is closed in ''U''. Equivalently, ''X'' is countably generated if and only if the closure of any subset ''A'' of ''X'' equals the union of closures of all countable subsets of ''A''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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