line-compact

Definition

• Let K be a convex subset of a linear topological space X. We say that K is line-compact if L∩K is a compact subset of L (in its unique linear topology) for every line L in X.

Property

• if K is σ-convex and line-closed, K is line-compact.

Reference

• Rosenthal, Haskell, L^1-convexity. Functional analysis, 156--174, Lecture Notes in Math., 1332, Springer, Berlin, 1988.