Definition
- A line-bounded convex subset K of a linear topoIogical space X is said to be σ-line-compact if the following holds: let be sequences in K so that there exist positive scalars with so that for all n , and where Then both converge to elements of K.
Property
- Every σ-line-compact set is line-compact.
Reference
- Rosenthal, Haskell, L^1-convexity. Functional analysis, 156--174, Lecture Notes in Math., 1332, Springer, Berlin, 1988.