By Alaine Low

In lots of international locations in Africa and Asia, rotating reductions and credits institutions underpin a lot of the financial system. This survey covers the big variety of literature on those institutions. released through Centre for Cross-Cultural learn on girls.

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The next result is referred to as the Banach-Steinhaus closure theorem . 3 Let X be a TVS with the t-property, Y a TVS, and {fn } a pointwise bounded sequence of continuous linear maps from X to Y. Iim f (x) = f(x) n-и» Let x € X Then f is continuous and linear. Now we have (cf. Ref. c. TVS. Then X is a W-space if and only if any of the following conditions is satisfied: (i) Each barrel in X is bornivorous. Chap. I 28 (ii) Each a(X*,X)-bounded sequence in X* is 3(X*,X)-bounded. c. TVS is uniformly bounded on bounded sets.

C. TVS. Suppose S is the family of all precompact (balanced, convex, and compact subsets) of X; then the corre sponding S-topology on X* is denoted by A(X*,X)[к(X*,X)] . Let S be the family of all balanced, convex, and к (X*,X)-compact subsets of X*; then the corresponding S-topology on X is denoted by y(X,X*). c. TVS. The finest topology (finest locally convex topology) on X* which induces on every equicontinuous sub set of X* the same topology as a(X*,X) is denoted by v(X*,X)[y(X*,X)] . Remark: As pointed out by Komura [138], the topology v(X*,X) is not necessarily a linear topology on X*.

C. TVS is uniformly bounded on bounded sets. c. c. TVS X is a W-space if and only if X and (X,ß(X,X*)) have the same bounded sets. c. TVS X is a W-space if and only if (X*,a(X*,X)) is a W-space. We recall the following device due to Grothendieck for getting normed spaces out of a TVS X. c. TVS X; then sp {A> = IKnA : n > I) and we denote it by Хд. Let qA represent the Minkowski functional of A. If A is also bounded, then (Хд»Чд) is a normed space, and if in addition to this A is sequentially complete, then (Хд*Чд) is a Banach space (Ref.