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In mathematics, a **topological module** is a module over a topological ring such that scalar multiplication and addition are continuous.

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

An abelian topological group can be considered as a topological module over where 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 -adic topology on a ring and its modules. Let be an ideal of a ring The sets of the form for all and all positive integers form a base for a topology on that makes into a topological ring. Then for any left -module the sets of the form for all and all positive integers form a base for a topology on that makes into a topological module over the topological ring

- Linear topology
- Ordered topological vector space
- Topological abelian group
- Topological field
- Topological group – Group that is a topological space with continuous group action
- Topological ring
- Topological semigroup
- 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.