Countably generated

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In mathematics, the term countably generated can have several meanings:

  • An algebraic structure (group, module, algebra) having countably many generators, see generating set
  • Countably generated space, a topological space in which the topology is determined by its countable subsets
  • Countably generated module. (Kaplansky's theorem says that a projective module is a direct sum of countably generated modules.)