Comments on the KKM theory on hyperconvex metric spaces

KKM and Ky Fan Theorems in Hyperconvex Metric Spaces

In hyperconvex metric spaces, we introduce Knaster-KuratowskiMazurkiewicz mappings (in short KKM-maps). Then we prove an analogue to Ky Fan fixed point theorem in hyperconvex metric spaces.

Hyperconvex Semi-metric Spaces

We examine the close analogy which exists between Helly graphs and hyperconvex metric spaces, and propose the hyperconvex semi-metric space as an unifying concept. Unlike the metric spaces, these semi-metric spaces have a rich theory in the discrete case. Apart from some new results on Helly graphs, the main results concern: fixed point property of contractible semi-metric spaces (for nonexpans...

Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We bel...

On Some Properties of Hyperconvex Spaces

We are going to answer some open questions in the theory of hyperconvex metric spaces. We prove that in complete R-trees hyperconvex hulls are uniquely determined. Next we show that hyperconvexity of subsets of normed spaces implies their convexity if and only if the space under consideration is strictly convex. Moreover, we prove a Krein-Milman type theorem for Rtrees. Finally, we discuss a ge...

Some result on modular hyperconvex spaces