Linear topology

Not to be confused with Linear bus topology.

In algebra, a linear topology on a left $A$-module $M$ is a topology on $M$ that is invariant under translations and admits a fundamental system of neighborhood of $0$ that consists of submodules of $M.$ If there is such a topology, $M$ is said to be linearly topologized. If $A$ is given a discrete topology, then $M$ becomes a topological $A$-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 – topological group whose group is abelianPages 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.