On compact subsets in coechelon spaces of infinite order

On Weakly Compact Subsets of Banach Spaces

Introduction. The two sections of this note are independent, but they are related by the fact that both use the results of [5 ] to obtain information on the properties of weakly compact sets in Banach spaces. In the first section we prove some results on a class of compact sets which is believed to include all weakly compact subsets of Banach spaces. We are interested in the properties of the n...

Domain representations of spaces of compact subsets

Compact Subsets of Spaces of Holomorphic Functions

In [1] compactness criteria in function spaces are investigated for general coorbit spaces. As an application it is shown that a bounded and closed subset A ⊂ F := {f : f is entire and Z C |f(z)|2e−|z| dλ(z) < ∞} is compact if and only if ∀2 > 0 ∃ a compact subset C ⊂ Cn with Z CC |f(z)|2e−|z| dλ(z) < 2 ∀f ∈ A. The methods of [1] cannot be easily adopted for the spaces Fm := {f : f is entire an...

Maximizing an interval order on compact subsets of its domain

Maximal elements of a binary relation on compact subsets of a metric space define a choice function. An infinite extension of transitivity is necessary and sufficient for such a choice function to be nonempty-valued and path independent (or satisfy the outcast axiom). An infinite extension of acyclicity is necessary and sufficient for the choice function to have nonempty values provided the und...

Zone diagrams in compact subsets of uniformly convex normed spaces

A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matoušek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and...