Linear topology

In algebra, a linear topology on a left A {\displaystyle A} -module M {\displaystyle M} is a topology on M {\displaystyle M} that is invariant under translations and admits a fundamental system of neighborhood of 0 {\displaystyle 0} that consists of submodules of M . {\displaystyle M.} If there is such a topology, M {\displaystyle M} is said to be linearly topologized. If A {\displaystyle A} is given a discrete topology, then M {\displaystyle M} becomes a topological A {\displaystyle A} -module with respect to a linear topology.

See also

  • Ordered topological vector space
  • Ring of restricted power series – Formal power series with coefficients tending to 0Pages displaying short descriptions of redirect targets
  • Topological abelian group – concept in mathematicsPages displaying wikidata descriptions as a fallback
  • Topological field – Algebraic structure with addition, multiplication, and divisionPages displaying short descriptions of redirect targets
  • Topological group – Group that is a topological space with continuous group action
  • Topological module
  • Topological ring – ring where ring operations are continuousPages displaying wikidata descriptions as a fallback
  • Topological semigroup – semigroup with continuous operationPages displaying wikidata descriptions as a fallback
  • Topological vector space – Vector space with a notion of nearness

References

  • Bourbaki, N. (1972). Commutative algebra (Vol. 8). Hermann.


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