**The Existence of Unbounded Closed Convex Sets with Trivial Recession Cone in Normed Spaces **

* Huynh The Phung *

**Abstract**

Itâ€™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.