# Is there a non-compact Poulsen simplex?

A Choquet simplex is a closed, convex and metrizable subset of a locally convex Hausdorff topological vector space in which every point is a barycenter of a unique probability measure supported on the set of extreme points. The Poulsen simplex is a unique nontrivial compact Choquet simplex with a dense set of extreme points. This was proved by Lindenstrauss, Olsen and Sternfeld (Ann. Inst. Fourier (Grenoble) 28 (1978), no. 1, vi, 91–114); see also http://www.ams.org/mathscinet-getitem?mr=500918. The Poulsen simplex has many remarkable properties. Is there a similar object in the category of not necessarily compact (but bounded) Choquet simplices?

• consider the class of non-compact simplices that you consider small / finitary (simplices in $\mathbb{R}^n$ with removed boundary?),