Linear topology

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

See also

• Ordered topological vector space
• Topological abelian group
• 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.