View source for Linear topology

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

==See also==

* {{annotated link|Ordered topological vector space}}
* {{annotated link|Topological abelian group}}
* {{annotated link|Topological group}}
* {{annotated link|Topological module}}
* {{annotated link|Topological ring}}
* {{annotated link|Topological semigroup}}
* {{annotated link|Topological vector space}}

==References==

{{reflist}}

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

[[Category:Topology]]
[[Category:Topological algebra]]
[[Category:Topological groups]]


{{Sourceattribution|Linear topology}}