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Convex series

Published online by Cambridge University Press:  24 October 2008

G. J. O. Jameson
G. J. O. Jameson
Affiliation:
University of Warwick, Coventry, England
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Extract

1. Introduction. Let A be a subset of a Hausdorff topological linear space. By a convex series of elements of A we mean a series of the form where an∈A and λn ≥ 0 for each n, and . We say that A is:

(i) CS-closed if it contains the sum of every convergent convex series of its elements;

(ii) CS-compact if every convex series of its elements converges to a point of A (this bold terminology is chosen because sets satisfying this condition turn out to have properties analogous to those of compact sets).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 1 , July 1972 , pp. 37 - 47
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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