An invariant of convex structures âˆ’ the depth âˆ’ is used to study the structure of finite median graphs. The main result is a recursive description of graphs of given depth. This leads to a completeâ€¦ (More)

It is shown that a collapsible, compact, connected, simplicial polyhedron admits a cubical subdivision and a median convexity, such that all cubes are convex subspaces with a convexity of subcubes.â€¦ (More)

Dendrons and their products admit a natural, continuous median operator. We prove that there exists a two-dimensional metric continuum with a continuous median operator, for which there is noâ€¦ (More)

The median stabilization degree (msd, for short) of a median algebra measures the largest possible number of steps needed to generate a subalgebra with an arbitrary set of generators. With computerâ€¦ (More)

The superextension A(Z) of a normal space Z is the set of all maximal linked families of closed subsets of Z, equipped with a Waliman-type topology. This construction was first devised by De Grootâ€¦ (More)

S[ and Sg are then said to separate (or: to screen) SÂ± and S2. Finally, Sf is called a binary subbase if each linked system S^ (zS^ (i.e., a subcollection S^' of ^ of which any two members meet)â€¦ (More)