Subject: Re: questions about top'l gps Date: Mon, 2 Aug 2004 10:58:54 -0500 (CDT) From: "Carlos Prieto (113)" To: Don Davis Dear Don, with respect to question 2 of Adel's, I believe that the answer is yes (not only for topological groups, but for any category that has limits) provided that one has an obvious compatibility of the different morphisms appearing in the inverse systems. One can take a look at the very end of Chapter IX (Special Limits) of Mac Lane's Categories for the Working Mathematician (I checked the German version). Kind regards, Carlos Prieto ================================================== On Mon, 2 Aug 2004, Don Davis wrote: > Subject: Re:Questions > Date: Fri, 30 Jul 2004 08:22:58 -0700 (PDT) > From: adel george > > From:Dr.George,Adel A. > > I have the following questions. > 1. Let G be a topological group which is the > inverse limit of locally compact(Lie) groups,does > every neighbourhood of the identity element in G > contain a closed normal subgroup H such that G/H is > locally compact(Lie) group? > 2. Let G be a topological group which is the > inverse limit of groups each of which is an inverse > limit of locally compact(Lie) groups.Is G an inverse > limit of locally compact(Lie) groups? > Thank you. > > > -- =================== PROF. CARLOS PRIETO Instituto de Matemáticas, UNAM 04510 México, DF, MÉXICO cprieto@math.unam.mx Tel. (++52-55) 5622-4489,-4520 Fax (++52-55) 5616 0348 =======================