Acta Mathematica Vietnamica
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The Existence of Unbounded Closed Convex Sets with Trivial Recession Cone in Normed Spaces
Huynh The Phung
Abstract
It’s well known that a closed convex set in a finite-dimensional normed space is unbounded if and only if it has a nonzero recession direction. In this work, we shall prove that in every infinite-dimensional normed space there exists an unbounded closed convex set whose recession cone consists of the zero vector alone.