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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).

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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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