Settore scientifico disciplinare di riferimento | (MAT/03) |

Ateneo | Università degli Studi di ROMA "La Sapienza" |

Struttura di afferenza | Dipartimento di MATEMATICA |

Recapiti | Elenco recapiti telefonici |

attilio.ledonne@uniroma1.it |

Curriculum scientifico Attilio Le Donne:

On chaotic extensions of dynamical systems

Alessandro Fedeli, Attilio Le Donne

In this paper, inspired by some results in linear dynamics, we will show that every dynamical system (X,f), where f is a continuous self-map on a separable metric space X, can be extended to a chaotic (in the sense of Devaney) dynamical system in an isometric way.

Journal: Topology and Its Applications - TOPOL APPL , vol. 158, no. 4, pp. 594-596, 2011

On a question of Mauldin and Ulam concerning homeomorphisms

Alessandro Fedeli, Attilio Le Donne

In this paper we solve a question of Mauldin and Ulam about transformations preserving homeomorphic pairs.

Journal: Topology and Its Applications - TOPOL APPL , vol. 158, no. 16, pp. 2122-2124, 2011

On metric spaces and local extrema (Citations: 7)

Alessandro Fedeli, Attilio Le Donne

The main aim of this paper is to give a positive answer to a question of Behrends, Geschke and Natkaniec regarding the existence of a connected metric space and a non-constant real-valued continuous function on it for which every point is a local extremum. Moreover we show that real-valued continuous functions on connected spaces such that every ...

Journal: Topology and Its Applications - TOPOL APPL , vol. 156, no. 13, pp. 2196-2199, 2009

A note on the uniform limit of transitive dynamical systems

Alessandro Fedeli, Attilio Le Donne

In this note we study the dynamical behaviour of the uniform limit of a sequence of continuous self-maps on a compact metric space satisfying (topological) transitivity or other related properties. Moreover, some conditions for the transitivity of a limit are given.

Journal: Bulletin of The Belgian Mathematical Society-simon Stevin - BULL BELG MATH SOC-SIMON STEV , vol. 16, no. 2009, pp. 59-66, 2009

On almost periodic orbits and minimal sets (Citations: 2)

Alessandro Fedeli, Attilio Le Donne

In this short note we solve in the negative the three problems recently posed by Jie-Hua Mai and Wei-Hua Sun regarding the behaviour of almost periodic orbits and minimal sets of dynamical systems whose phase space is not regular.

Journal: Topology and Its Applications - TOPOL APPL , vol. 156, no. 2, pp. 473-475, 2008

ON LIE BIALGEBRAS OF LOOPS ON ORIENTABLE SURFACES

ATTILIO LE DONNE

Journal: Journal of Knot Theory and Its Ramifications - JKTR , vol. 17, no. 03, 2008

The fine structure of strong disconnectedness properties

Alessandro Fedeli, Attilio Le Donne

In this paper we introduce a general notion of disconnectedness and show how it is related to some classical disconnectedness properties. Several new properties are introduced and investigated, and some open problems are posed.

Journal: Chaos Solitons & Fractals - CHAOS SOLITON FRACTAL , vol. 23, no. 2, pp. 677-682, 2005

On a problem related to a non-squeezing theorem

Alessandro Fedeli, Attilio Le Donne

In this paper we give a solution to a problem of Kulpa about the interior of the image of certain continuous maps f:X→Rn where X is a compact subset of Rn with non-empty interior. Moreover we show that the image of every continuous map f:X→R2 where X is a non-empty compact subset of R2 and diamf−1f(...

Journal: Topology and Its Applications - TOPOL APPL , vol. 148, no. 1, pp. 33-38, 2005

On Lie bialgebras of loops on orientable surface

Attilio Le Donne

Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6)(1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of loops on an orientable surface. Chas (Combinatorial Lie bialgebras of curves on surfaces, Topology 43 (2004) 543), by the aid of the computer, found ...

Published in 2005.

On Lie bialgebras of loops on orientable surface

Attilio Le Donne

Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6)(1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of loops on an orientable surface. Chas (Combinatorial Lie bialgebras of curves on surfaces, Topology 43 (2004) 543), by the aid of the computer, found ...

Published in 2005.

Partial n-point sets and zero-dimensionality (Citations: 1)

Attilio Le Donne

In this paper we show that every one-dimensional partial n-point set in higher dimensions contains arcs. This answers a question posed by Dijkstra and van Mill.

Journal: Topology and Its Applications - TOPOL APPL , vol. 128, no. 2, pp. 169-172, 2003

On good connected preimages (Citations: 3)

Alessandro Fedeli, Attilio Le Donne

In this paper we investigate when a connected space has a connected preimage with some additional properties. In particular we completely characterize the continuous and the quotient images of metric connected spaces. Our results answer several problems posed by V.V. Tkachuk.

Journal: Topology and Its Applications - TOPOL APPL , vol. 125, no. 3, pp. 489-496, 2002

Connectedness properties of special subsets of the plane (Citations: 3)

Alessandro Fedeli, Gary Gruenhage, Attilio Le Donne

In this paper we investigate the connectedness properties of graphs of functions from the real line R to itself. We show, among other things, that (i) a totally disconnected graph of a function from R to R need not be zero-dimensional, (ii) the graph of every injection from R to R is zero-dimensional provided that it does not ...

Journal: Topology and Its Applications - TOPOL APPL , vol. 117, no. 1, pp. 1-7, 2002

Pytkeev spaces and sequential extensions (Citations: 1)

Alessandro Fedeli, Attilio Le Donne

In this paper we construct, in response to a question of Malykhin and Tironi, a ZFC example of a perfectly normal Pytkeev space which has no sequential extensions.

Journal: Topology and Its Applications - TOPOL APPL , vol. 117, no. 3, pp. 345-348, 2002

Dense embeddings in ( pathwise ) connected spaces : results and open problems

Attilio Le Donne

Published in 2001.

Embeddings into normal first countable spaces

Alessandro Fedeli, Attilio Le Donne

In this paper we construct, in response to a question of Arhangel'skiı̌, a zero-dimensional first countable space which cannot be embedded into a normal first countable space.

Journal: Topology and Its Applications - TOPOL APPL , vol. 111, no. 1, pp. 135-137, 2000

Dense embeddings in pathwise connected spaces (Citations: 3)

Alessandro Fedeli, Attilio Le Donne

This paper is devoted to the problem of finding those T1-spaces (Hausdorff spaces) which are densely embeddable in a pathwise connected T1-space (Hausdorff space). In particular, we prove that a countable first countable Hausdorff space (with more than one point) is pathwise connectifiable (i.e., it can be densely embedded in a pathwise connected Hausdorff space) if and ...

Journal: Topology and Its Applications - TOPOL APPL , vol. 96, no. 1, pp. 15-22, 1999

On locally connected connectifications (Citations: 2)

Alessandro Fedeli, Attilio Le Donne

A connected Hausdorff space Y is called a connectification of a space X if X can be densely embedded in Y. This paper is a contribution to the problem of finding those spaces which have a locally connected connectification. The results obtained imply a positive answer to the following questions of Alas, Tkačenko, Tkachuk and Wilson:(i) Does the Sorgenfrey ...

Journal: Topology and Its Applications - TOPOL APPL , vol. 96, no. 1, pp. 85-88, 1999

An independency result in connectification theory

Alessandro Fedeli, Attilio Le Donne

A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let be the following statement: "a perfect T3-space X with no more than 2 c clopen subsets is connectifiable if and only if no proper nonempty clopen subset of X is feebly compact". In this note we show that neither nor ¬ is ...

Published in 1999.

Connectifications of metrizable spaces (Citations: 1)

Gary Gruenhage, John Kulesza, Attilio Le Donne

We answer a question of Alas, Tkačenko, Tkachuk, and Wilson by constructing a metrizable space with no compact open subsets which cannot be densely embedded in a connected metrizable (or even perfectly normal) space. We also obtain a result that implies that every nowhere locally compact metrizable space can be densely embedded in a connected metrizable space.

Journal: Topology and Its Applications - TOPOL APPL , vol. 82, no. 1, pp. 171-179, 1998

Weak ?-property in Σ-products

A Le Donne

Journal: Topology and Its Applications - TOPOL APPL , vol. 60, no. 3, pp. 229-233, 1994

THE SORGENFREY LINE HAS A LOCALLY PATHWISE CONNECTED CONNECTIFICATION (Citations: 1)

Alessandro Fedeli, Attilio Le Donne

Abstract. We answer a question of Alas, Tka cenko, Tkachuk and Wilson by constructing a connected locally pathwise connected Hausdor,space in which the Sorgenfrey line can be densely embedded. A connectication of a T2-space X is a connected Hausdor space Y in which X