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In mathematics, a topological module is a module over a topological ring such that scalar multiplication and addition are continuous. == Examples == A topological vector space is a topological module over a topological field. An abelian topological group can be considered as a topological module over Z, where 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 ''I''-adic topology on a ring and its modules. Let ''I'' be an ideal of a ring ''R''. The sets of the form , for all ''x'' in ''R'' and all positive integers ''n'', form a base for a topology on ''R'' that makes ''R'' into a topological ring. Then for any left ''R''-module ''M'', the sets of the form , for all ''x'' in ''M'' and all positive integers ''n'', form a base for a topology on ''M'' that makes ''M'' into a topological module over the topological ring ''R''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Topological module」の詳細全文を読む スポンサード リンク
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