Vassilis Kanellopoulos

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The research presented in this paper was motivated by our aim to study a problem due to J. Bourgain [3]. The problem in question concerns the uniform boundedness of the classical separation rank of the elements of a separable compact set of the first Baire class. In the sequel we shall refer to these sets (separable or non-separable) as Rosenthal compacta(More)
A tree T is said to be homogeneous if it is uniquely rooted and there exists an integer b > 2, called the branching number of T , such that every t ∈ T has exactly b immediate successors. A vector homogeneous tree T is a finite sequence (T1, ..., Td) of homogeneous trees and its level product ⊗T is the subset of the cartesian product T1 × ...× Td consisting(More)
For every integer k > 2 let [k]<N be the set of all words over k. A Carlson–Simpson tree of [k]<N of dimension m > 1 is a subset of [k]<N of the form {w} ∪ { ww0(a0) ...wn(an) : n ∈ {0, ...,m− 1} and a0, ..., an ∈ [k] } where w is a word over k and (wn) m−1 n=0 is a finite sequence of left variable words over k. We study the behavior of a family of(More)
A tree T is said to be homogeneous if it is uniquely rooted and there exists an integer b > 2, called the branching number of T , such that every t ∈ T has exactly b immediate successors. We study the behavior of measurable events in probability spaces indexed by homogeneous trees. Precisely, we show that for every integer b > 2 and every integer n > 1(More)
We show that for every rooted, finitely branching, pruned tree T of height ω there exists a family F which consists of order isomorphic to T subtrees of the dyadic tree C = {0, 1}<N with the following properties: (i) the family F is a Gδ subset of 2C ; (ii) every perfect subtree of C contains a member of F ; (iii) if K is an analytic subset of F , then for(More)
Let ε > 0 and F be a family of finite subsets of the Cantor set C. Following D. H. Fremlin, we say that F is ε-filling over C if F is hereditary and for every F ⊆ C finite there exists G ⊆ F such that G ∈ F and |G| ≥ ε|F |. We show that if F is ε-filling over C and C-measurable in [C], then for every P ⊆ C perfect there exists Q ⊆ P perfect with [Q] ⊆ F . A(More)
As the polymer industry becomes more global and competitive pressures are intensifying, polymer manufacturers recognize the need for the development of advanced process simulators for polymer plants. The overall goal is to utilize powerful, flexible, adaptive design and predictive simulation tools that can follow and predict the behaviour of polymer(More)