Quadratic forms and linear topologies. On completions
نویسندگان
چکیده
منابع مشابه
Notes on Filtrations, Topologies, and Completions
(i) G is Hausdorff. (ii) Points in G are closed. (iii) The Gi intersect in {e}. Of course, (i) implies (ii) by general topology. For (ii) implies (i), the diagonal in G×G is μ(e), where μ(g, h) = gh. Since G−Gi is the union of the cosets gGi with g / ∈ Gi, G−Gi is open, hence G−Gi is both open and closed, hence so is Gi. Now (iii) clearly implies (ii). If x is in all Gi and is not e, then there...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Series A I Mathematica
سال: 1975
ISSN: 0066-1953
DOI: 10.5186/aasfm.1975.584