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Papers by Paolo Vitolo

Research paper thumbnail of When is Kuratowski convergence topological?

Research paper thumbnail of The reconstruction of simply disconnected tournaments

In this paper we will prove that simply disconnected tournaments of order at least 7 are reconstr... more In this paper we will prove that simply disconnected tournaments of order at least 7 are reconstructible, i.e. they are determined (up to isomorphisms) by their subtournaments.

Research paper thumbnail of Decomposition of topologies on lattices and hyperspaces

Dissertationes Mathematicae

Research paper thumbnail of The representation of weighted quasi-metric spaces

Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

In this note we continue the investigation carried out in [Topology Appl. 65, No. 1, 101-104 (199... more In this note we continue the investigation carried out in [Topology Appl. 65, No. 1, 101-104 (1995; Zbl 0828.54024)]. We show that every weighted quasi-metric space can be identified with a subspace of a space of some canonical type, which is constructed from a metric space. We also present a very simple method to construct a weighted quasi-metric space, as the graph of a function defined on a metric space, and show that every weighted quasi-metric space arises in this way. Similar results may be obtained if we drop the requirement that the weight function have nonnegative values.

Research paper thumbnail of Compatibility and central elements in pseudo-effect algebras

Research paper thumbnail of A representation theorem for quasi-metric spaces

Topology and its Applications, 1995

Research paper thumbnail of A generalization of set-difference

Mathematica Slovaca, 2011

Research paper thumbnail of A question about basic algebras

Algebra universalis, 2009

Research paper thumbnail of Decomposition of Pseudo-effect Algebras and the Hammer–Sobczyk Theorem

Research paper thumbnail of Decomposition of effect algebras and the Hammer�Sobczyk theorem

Algebra Universalis, 2009

Research paper thumbnail of Extension of measures on pseudo-D-lattices

Mathematica Slovaca, 2016

Research paper thumbnail of Positive Operators � la Aumann-Shapley on Spaces of Functions on D-Lattices

Research paper thumbnail of Lyapunov decomposition of measures on effect algebras

Research paper thumbnail of Bornological Convergences on the Hyperspace of a Uniformizable Space

Set-Valued and Variational Analysis, 2016

ABSTRACT Bornological convergence is a generalization of the well known Attouch--Wets convergence... more ABSTRACT Bornological convergence is a generalization of the well known Attouch--Wets convergence. Our aim is to compare lower, upper and ``two-sided'' convergences generated by two compatible uniformities and two arbitrary bornologies. Moreover, the comparison of convergences induced by bounded-proximal topologies is characterized.

Research paper thumbnail of Tightness, character and related properties of hyperspace topologies

Research paper thumbnail of Decomposition of Pseudo-effect Algebras and the Hammer–Sobczyk Theorem

Research paper thumbnail of On the Aumann-Shapley value

Research paper thumbnail of Decomposition and control theorems in effect algebras

Research paper thumbnail of Pseudo-D-lattices and separating points of measures

Fuzzy Sets and Systems, 2015

Research paper thumbnail of Comparability of lower Attouch--Wets topologies

Filomat

Beer and Di Concilio have given necessary and sufficient conditions for a two-sided Attouch--Wets... more Beer and Di Concilio have given necessary and sufficient conditions for a two-sided Attouch--Wets topology to contain another on the hyperspace of non-empty closed subsets of a metrizable space as determined by metrics compatible with the topology. In the present paper, we characterize comparability of lower Attouch--Wets topologies as determined by compatible metrics.

Research paper thumbnail of When is Kuratowski convergence topological?

Research paper thumbnail of The reconstruction of simply disconnected tournaments

In this paper we will prove that simply disconnected tournaments of order at least 7 are reconstr... more In this paper we will prove that simply disconnected tournaments of order at least 7 are reconstructible, i.e. they are determined (up to isomorphisms) by their subtournaments.

Research paper thumbnail of Decomposition of topologies on lattices and hyperspaces

Dissertationes Mathematicae

Research paper thumbnail of The representation of weighted quasi-metric spaces

Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

In this note we continue the investigation carried out in [Topology Appl. 65, No. 1, 101-104 (199... more In this note we continue the investigation carried out in [Topology Appl. 65, No. 1, 101-104 (1995; Zbl 0828.54024)]. We show that every weighted quasi-metric space can be identified with a subspace of a space of some canonical type, which is constructed from a metric space. We also present a very simple method to construct a weighted quasi-metric space, as the graph of a function defined on a metric space, and show that every weighted quasi-metric space arises in this way. Similar results may be obtained if we drop the requirement that the weight function have nonnegative values.

Research paper thumbnail of Compatibility and central elements in pseudo-effect algebras

Research paper thumbnail of A representation theorem for quasi-metric spaces

Topology and its Applications, 1995

Research paper thumbnail of A generalization of set-difference

Mathematica Slovaca, 2011

Research paper thumbnail of A question about basic algebras

Algebra universalis, 2009

Research paper thumbnail of Decomposition of Pseudo-effect Algebras and the Hammer–Sobczyk Theorem

Research paper thumbnail of Decomposition of effect algebras and the Hammer�Sobczyk theorem

Algebra Universalis, 2009

Research paper thumbnail of Extension of measures on pseudo-D-lattices

Mathematica Slovaca, 2016

Research paper thumbnail of Positive Operators � la Aumann-Shapley on Spaces of Functions on D-Lattices

Research paper thumbnail of Lyapunov decomposition of measures on effect algebras

Research paper thumbnail of Bornological Convergences on the Hyperspace of a Uniformizable Space

Set-Valued and Variational Analysis, 2016

ABSTRACT Bornological convergence is a generalization of the well known Attouch--Wets convergence... more ABSTRACT Bornological convergence is a generalization of the well known Attouch--Wets convergence. Our aim is to compare lower, upper and ``two-sided'' convergences generated by two compatible uniformities and two arbitrary bornologies. Moreover, the comparison of convergences induced by bounded-proximal topologies is characterized.

Research paper thumbnail of Tightness, character and related properties of hyperspace topologies

Research paper thumbnail of Decomposition of Pseudo-effect Algebras and the Hammer–Sobczyk Theorem

Research paper thumbnail of On the Aumann-Shapley value

Research paper thumbnail of Decomposition and control theorems in effect algebras

Research paper thumbnail of Pseudo-D-lattices and separating points of measures

Fuzzy Sets and Systems, 2015

Research paper thumbnail of Comparability of lower Attouch--Wets topologies

Filomat

Beer and Di Concilio have given necessary and sufficient conditions for a two-sided Attouch--Wets... more Beer and Di Concilio have given necessary and sufficient conditions for a two-sided Attouch--Wets topology to contain another on the hyperspace of non-empty closed subsets of a metrizable space as determined by metrics compatible with the topology. In the present paper, we characterize comparability of lower Attouch--Wets topologies as determined by compatible metrics.

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