By a topological abelian group T (t.a.g. T) we shall mean an abstract abelian group-written additively-such that (a) the function x + y and the inverse function -x are continuous functions (neighborhood continuity) of both variables x and y and of the variable x, respectively, with respect to a postulated Hausdorff topology; (b) given any y ε T and any Hausdorff neighborhood U of 0 ε T, there exists a "positive integer" n such that y ε nU. ududIn this note we shall give brief indications of a differential calculus for functions f(x) with x e t.a.g. T_1 and values in a t.a.g. T_2. Proofs and furtheruddevelopments will appear elsewhere.
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机译：拓扑阿贝尔群T（标记T）是指抽象阿贝尔群加法写的-（a）函数x + y和反函数-x是变量x和y的连续函数（邻域连续性）相对于假定的Hausdorff拓扑分别为变量x和。 （b）给定yεT和0εT的任何Hausdorff邻域U，存在一个“正整数” n使得yεnU。 ud ud在本说明中，我们将简要说明函数f（x）与x e t.a.g的微积分。 T_1和t.a.g.中的值T_2。证明和进一步的发展将在其他地方出现。
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