In mathematics, the restricted product is a construction in the theory of topological groups.
Let be an index set; a finite subset of . If is a locally compact group for each , and is an open compact subgroup for each , then the restricted product
is the subset of the product of the 's consisting of all elements such that for all but finitely many .
This group is given the topology whose basis of open sets are those of the form
where is open in and for all but finitely many .
One can easily prove that the restricted product is itself a locally compact group. The best known example of this construction is that of the adele ring and idele group of a global field.
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achievement of particular product-development milestones, earnings per share goals or other financial targets. Restricted stock is a popular alternative...
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list of authorized and restricted substances for cosmetic use, used in products such as hair dyes, nail hardeners, or used as product preservatives. Most...
to age restrictedproducts including cigarettes and alcoholic beverages. Under the scheme, customers attempting to buy age-restrictedproducts are asked...
Within the field of organic chemistry, the definition of natural products is usually restricted to organic compounds isolated from natural sources that are...
number of enterprises is small, entry and exit from the market are restricted, product attributes are different, and the demand curve is downward sloping...
drinks and withdraw existing items immediately. The sale of the restrictedproducts during this period carried a penalty of 30-day suspension of liquor...
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as proof of age when a German citizen attempts to purchase an age-restrictedproduct and insists on the production of a Dutch-issued passport or driving...
{\displaystyle \mathbb {Q} } where the symbol ′ {\displaystyle '} means restrictedproduct. That is, an element is a sequence that is integral except at a finite...
Under EU regulations only Spain and Portugal can label their product as Sangria; similar products from different regions are differentiated in name. Clericó...
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