Linear topology

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

See also[]

• Ordered topological vector space
• Ring of restricted power series
• Topological abelian group
• Topological field
• Topological group – Group that is a topological space with continuous group action
• Topological module
• Topological ring
• Topological semigroup
• Topological vector space – Vector space with a notion of nearness

References[]

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

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