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restricted direct product
Let be a collection of locally compact topological groups. For all but finitely many , let be a compact open subgroup of . The restricted direct product of the collection with respect to the collection is the subgroup
of the direct product .
We define a topology on as follows. For every finite subset that contains all the elements for which is undefined, form the topological group
consisting of the direct product of the ’s, for , and the ’s, for . The topological group is a subset of for each such , and we take for a topology on the weakest topology such that the are open subsets of , with the subspace topology on each equal to the topology that already has in its own right.
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:
Mathematics Subject Classification
11R56 Adèle rings and groups22D05 General properties and structure of locally compact groups
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new question: Taylor's Series Query! by unlord
new question: Laplace transform by J
new question: Residue Calculus by J
May 19
new Education: Project: PlanetMath Outlines Series by unlord
May 17
new image: sinx_approx.png by jeremyboden
new image: approximation_to_sinx by jeremyboden
new image: approximation_to_sinx by jeremyboden


