Convex series
1972 ◽
Vol 72
(1)
◽
pp. 37-47
◽
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).
1967 ◽
Vol 63
(2)
◽
pp. 311-313
◽
Keyword(s):
1972 ◽
Vol 72
(1)
◽
pp. 7-9
Keyword(s):
1988 ◽
Vol 11
(3)
◽
pp. 585-588
1989 ◽
Vol 106
(2)
◽
pp. 277-280
◽
1969 ◽
Vol 66
(3)
◽
pp. 541-545
◽
Keyword(s):
1968 ◽
Vol 64
(2)
◽
pp. 335-340
◽
Keyword(s):
2006 ◽
Vol 2006
◽
pp. 1-7
Keyword(s):