# Questions tagged [convexity-spaces]

Intended for questions about convexity spaces: convex hulls; convexity preserving and convex-to-convex functions; isomorphism of convexity spaces; (Chepoi's) separation axioms S1, S2, S3, and S4; interval convexities; subbasis and basis of convexities and topics alike. When considering (usual) convex sets in vector spaces, please use the [convex-analysis] tag.

12 questions
Filter by
Sorted by
Tagged with
95 views

52 views

### Reflexive and strictly convex but not uniform convex

I’m struggling with one question, I can find that authors are writing over uniform convex in Banach spaces a lot but still I haven’t found a good exampel for this: If space X is reflexive and strictly ...
40 views

### Convexity of a scaled multivariate digamma function

The problem... Let $\psi_p(a) = \frac{\partial \Gamma_p(a)}{\partial a}$ be the multivariate digamma function. I believe the following function to be strictly convex at least for real values $a>2p$...
218 views

### Are convex polytopes closed in arbitrary metric spaces?

Let $(X,d)$ be a metric space. For all points $x,y \in X$ we define the metric segment between them as the following set: $$\left [ x,y \right ] = \left \{ z \in X : d(x,z)+d(z,y)=d(x,y)\right \}$$ ...
• 1,323
337 views

### Convex hull of open sets is an open set?

Let $(X,d)$ be a metric space. For all points $x,y \in X$ we define the metric segment between them as the following set: $$\left [ x,y \right ] = \left \{ z \in X : d(x,z)+d(z,y)=d(x,y)\right \}$$ ...
• 1,323
393 views

### Topology basis consisting of convex sets in metric spaces

Let $(X,d)$ be a metric space. For all points $x,y \in X$ we define the metric segment between them as the following set: $$\left [ x,y \right ] = \left \{ z \in X : d(x,z)+d(z,y)=d(x,y)\right \}$$ ...
• 1,323
566 views

### Closure and interior of convex set is convex?

For a metric space $(X,d)$ and points $x,y \in X$ we define the metric segment between them as the following set: $\left [ x,y \right ] = \left \{ z \in X : d(x,z)+d(z,y)=d(x,y)\right \}$ We then say ...
• 1,323
377 views

### Are metric segments convex?

For a metric space $(X,d)$ and points $x,y \in X$ we define the metric segment between them as the following set: $\left [ x,y \right ] = \left \{ z \in X : d(x,z)+d(z,y)=d(x,y)\right \}$ Can we say ...
• 1,323