A topological vector space is a topological module over a topological field.

An abelian topological group can be considered as a topological module over ${\displaystyle \mathbb {Z} ,}$  where ${\displaystyle \mathbb {Z} }$  is the ring of integers with the discrete topology.

A topological ring is a topological module over each of its subrings.

A more complicated example is the ${\displaystyle I}$ -adic topology on a ring and its modules. Let ${\displaystyle I}$  be an ideal of a ring ${\displaystyle R.}$  The sets of the form ${\displaystyle x+I^{n}}$  for all ${\displaystyle x\in R}$  and all positive integers ${\displaystyle n,}$  form a base for a topology on ${\displaystyle R}$  that makes ${\displaystyle R}$  into a topological ring. Then for any left ${\displaystyle R}$ -module ${\displaystyle M,}$  the sets of the form ${\displaystyle x+I^{n}M,}$  for all ${\displaystyle x\in M}$  and all positive integers ${\displaystyle n,}$  form a base for a topology on ${\displaystyle M}$  that makes ${\displaystyle M}$  into a topological module over the topological ring ${\displaystyle R.}$ 

• Linear topology
• Ordered topological vector space
• 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 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

• Kuz'min, L. V. (1993). "Topological modules". In Hazewinkel, M. (ed.). Encyclopedia of Mathematics. Vol. 9. Kluwer Academic Publishers.