Topological Ring
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a topological ring is a ring R which is also a topological space such that both the addition and the multiplication are continuous as maps R × R R, where R × R carries the product topology. The group of units of R may not be a topological group using the subspace topology, as inversion on the unit group need not be continuous with the subspace topology. (An example of this situation is the adele ring of a global field. Its unit group, called the idele…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a topological ring is a ring R which is also a topological space such that both the addition and the multiplication are continuous as maps R × R R, where R × R carries the product topology. The group of units of R may not be a topological group using the subspace topology, as inversion on the unit group need not be continuous with the subspace topology. (An example of this situation is the adele ring of a global field. Its unit group, called the idele group, is not a topological group in the subspace topology.) Embedding the unit group of R into the product R × R as (x,x-1) does make the unit group a topological group. (If inversion on the unit group is continuous in the subspace topology of R then the topology on the unit group viewed in R or in R × R as above are the same.)