: Mathematics: topological ring

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topological ring

In mathematics, a topological ring is a ring ${\\displaystyle R}$ that is also a topological space such that both the addition and the multiplication are continuous as maps: ${\\displaystyle R\ imes R\ o R}$ where ${\\displaystyle R\ imes R}$ carries the product topology. That means ${\\displaystyle R}$ is an additive topological group and a multiplicative topological semigroup. Topological rings are fundamentally related to topological fields and arise naturally while studying them, since for example completion of a topological field may be a topological ring which is not a field.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Topological_ring)

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