Countably generated space
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In mathematics, a topological space V is called countably generated if V is closed in X whenever for each countable subspace U of X the set is closed in U.
A quotient of countably generated space is again counably generated. Similarly, a topological sum of countably generated spaces is countably generated. Therefore the countably generated spaces form a coreflective subcategory of the category of topological spaces. They are the coreflective hull of all countable spaces.
All borel sets are countably generated.
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