Restricted product

Restricted product

The restricted product is a construction in the theory of topological groups.

Let I be an indexing set; S a finite subset of I. If for each iin I, G_i is a locally compact group, and for each iin Iackslash S, K_i subset G_i is an open compact subgroup, then the restricted product : {prod_i}' G_i, is the subset of the product of the G_i 's consisting of all elements (g_i)_{iin I} such that g_i in K_i for all but finitely many iin Iackslash S.

This group is given the topology whose basis of open sets are those of the form: prod_i A_i,, where A_i is open in G_i and A_i = K_i for all but finitely many i.

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.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • product — 1 *work, production, opus, artifact Analogous words: forming or form, fabrication, manufacturing or manu facture (see corresponding verbs at MAKE): article, object, *thing 2 Product, production, produce are comparable when they denote something… …   New Dictionary of Synonyms

  • Restricted Line Officer — Restricted Line Officers in the United States Navy and Navy Reserve are line officers who are not eligible for Command at Sea. There are many different types and communities, including Engineering Duty Officers, Aerospace Engineering Duty… …   Wikipedia

  • Restricted randomization — Many processes have more than one source of variation in them. In order to reduce variation in processes, these multiple sources must be understood, and that often leads to the concept of nested or hierarchical data structures. For example, in… …   Wikipedia

  • Restricted use pesticide — Because of safety concerns, some pesticides are not available to the general public in the United States. The Restricted Use classification restricts a product, or its uses, to use by a certificated pesticide applicator or under the direct… …   Wikipedia

  • Restricted representation — In mathematics, restriction is a fundamental construction in representation theory of groups. Restriction forms a representation of a subgroup from a representation of the whole group. Often the restricted representation is simpler to understand …   Wikipedia

  • Restricted partial quotients — In mathematics, and more particularly in the analytic theory of regular continued fractions, an infinite regular continued fraction x is said to be restricted , or composed of restricted partial quotients , if the sequence of denominators of its… …   Wikipedia

  • Surplus product — Part of a series on Marxism …   Wikipedia

  • U.S. Consumer Product Safety Commission — Consumer Product Safety Commission seal Agency overview Formed 1972 Employees …   Wikipedia

  • Gold exchange-traded product — Gold exchange traded products are exchange traded funds (ETFs), closed end funds (CEFs) and exchange traded notes (ETNs) that aim to track the price of gold. Gold exchange traded products are traded on the major stock exchanges including Zurich,… …   Wikipedia

  • new product development — NPD A marketing procedure in which new ideas are developed into viable new products or extensions to existing products or product ranges. New ideas, which are generated either internally (e. g. by scientific research) or by feedback from… …   Big dictionary of business and management

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”