geometry-topology / Convex geometry
Sabok asked whether the compact convex set $S'(X)$ attached to a separable metric space of diameter at most one is always a simplex, and whether $S'(\mathbb{U}_1)$ is the Poulsen simplex. Both answers are negative, with obstructions already visible for finite $X$ and for the Urysohn space.
Temporal state
No reconciled state yet.
Append-only history
Sabok asked whether the compact convex set $S'(X)$ attached to a separable metric space of diameter at most one is always a simplex, and whether $S'(\mathbb{U}_1)$ is the Poulsen simplex. Both answers are negative, with obstructions already visible for finite $X$ and for the Urysohn space.
Research memory
Sabok asked whether the compact convex set $S'(X)$ attached to a separable metric space of diameter at most one is always a simplex, and whether $S'(\mathbb{U}_1)$ is the Poulsen simplex. Both answers are negative, with obstructions already visible for finite $X$ and for the Urysohn space.
Evidence graph
No public relationships recorded yet.