Countably Generated

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.)

Other articles related to "countably, countably generated":

Standard Probability Space - A Criterion of Standardness - Additional Remarks
... not depend on the choice of Taking we get the property well known as being countably separated (but called separable in Itô 1984) ... Taking we get the property well known as being countably generated (mod 0), see (Durrett 1996, Exer ... Probability space Countably separated Countably generated Standard Interval with Lebesgue measure Yes Yes Yes Naive white noise No No No Perforated interval Yes Yes No Every ...
Countably Generated Space - 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 ... A quotient of countably generated space is again countably generated ...

Famous quotes containing the word generated:

    Here [in London, history] ... seemed the very fabric of things, as if the city were a single growth of stone and brick, uncounted strata of message and meaning, age upon age, generated over the centuries to the dictates of some now all-but-unreadable DNA of commerce and empire.
    William Gibson (b. 1948)