Extension criterion for continuous convexity preserving maps (Q2774511)

The paper deals with topological convexity spaces, i.e., topological spaces with an additional convexity structure in the sense of [\textit{M. L. J. van de Vel}, Theory of convex structures, North-Holland Math. Libr. 50 (1993; Zbl 0785.52001)]. NEWLINENEWLINENEWLINEThe main theorem gives a necessary and sufficient condition for extending continuous convexity preserving maps defined on some subsets of a topological convexity space and with values in a compact topological median space. This result can be viewed as a common generalization of Taimanov's extension criterion for topological spaces and Sikorski's criterion for Boolean algebras. Some applications to the theory of superextensions are given.