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

Examples

A module topology is the finest topology such that scalar multiplication and addition are continuous. A finitely generated module topology is a topological ring. Note that this general definition of a module topology does not need to have a ring structure, it merely needs the existence of addition and scalar multiplication.

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

An abelian topological group is the ring of integers with the discrete topology.

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

-adic topology be an ideal form a base

See also

References