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Topological ring

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In mathematics, a topological ring is a ring R {\displaystyle R} that is also a topological space such that both the addition and the multiplication are continuous as maps R × R → R {\displaystyle R\times R\to R} where R × R {\displaystyle R\times R} carries the product topology. This means R {\displaystyle R} is an additive topological group and a multiplicative topological semigroup.