4 papers
Choice free Fixed Point Property in separable Banach spaces
Vassilios Gregoriades
We show that the standard approach of minimal invariant sets, which applies Zorn's Lemma and is used to prove fixed point theorems for non-expansive mappings in Banach spaces can b…
Classes of Polish spaces under effective Borel isomorphism
Vassilios Gregoriades
We study the equivalence classes under isomorphism, otherwise effective-Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and…
One more recursive-theoretic characterization of the Topological Vaught Conjecture
Vassilios Gregoriades
We prove in ZF a recursive-theoretic characterization of the Topological Vaught Conjecture by revisiting the fact that orbits in Polish -spaces are Borel sets.
The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued function (Extended Abstract)
Vassilios Gregoriades
In this article we treat a notion of continuity for a multi-valued function F and we compute the descriptive set-theoretic complexity of the set of all x for which F is continuous…