Euclidean Convexity Cannot be Compactified.
Extension and Selection theorems in Topological spaces with a generalized convexity structure
Families of convex sets closed under intersections, homotheties and uniting increasing sequences of sets
Fixed points and selections of set-valued maps on spaces with convexity.
Fixed points for generalized nonexpansive mappings
Functional analysis on normed spaces: the Banach space comparison.
Generalized approximate midconvexity
Generalized convexity and optimization problems
Generalized midset properties characterize geodesic circles and intervals
Glued convexity spaces, frames and graphs
Gluings and closures
Hypergroups defined from a linear space
Illumination and visibility problems in terms of closure operators.
Konvexita (1. část)
Limits and colimits of convexity spaces
LNC points for m-convex sets.
Metrically convex functions in normed spaces
Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.
n-ary transit functions in graphs
n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergraph. Also n-ary all paths transit function is considered.
Nonempty intersection theorems minimax theorems with applications in generalized interval spaces.
Note On H-Convex Functions