Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2001) s2


Editorial policy The journal Rendiconti dell’Istituto di Matematica dell’università di Trieste publishes original articles in all areas of mathematics. Special regard is given to research papers, but attractive expository papers may also be considered for publication. The journal usually appears in one issue per year. Additional issues may however be published. In particular, the Managing Editors may consider the publication of supplementary volumes related to some special events, like conferences, workshops, and advanced schools. All submitted papers will be refereed. Manuscripts are accepted for review with the understanding that the work has not been published before and is not under consideration for publication elsewhere. Our journal can be obtained by exchange agreements with other similar journals.

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Recent Submissions

Now showing 1 - 5 of 14
  • Publication
    On Hyperbolic 3-Orbifolds of Small Volume and Small Heegaard Genus
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2001)
    Zimmermann, Bruno
    In the present note we shall give geometric descriptions of the orientable hyperbolic 3-orbifolds of smallest known volumes. As in the case of hyperbolic 3-manifolds, the hyperbolic 3-orbifolds of smallest volumes are still not known but there is some evidence that our list should be complete (however in some cases the volumes have not yet been computed). We note that the natural candidates for the ten orientable hyperbolic 3-manifolds of smallest volumes have been described in [6] (all of Heegaard genus two). In the following, we shall consider only orientable orbifolds. Computations of volumes are based on the recent papers [11], [9] and [14].
      941  1041
  • Publication
    How Many Closed Structures does the Construct PRAP Admit?
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2001)
    Sioen, Mark
    We will prove that the topological construct PRAP, introduced by E. and R. Lowen in [9] as a numerification supercategory of the construct PRTOP of convergence spaces and continuous maps, admits a proper class of monoidal closed structures. We will even show that under the assumption that there does not exist a proper class of measurable cardinals, it admits a proper conglomerate (i.e. one which is not codable by a class) of mutually non-isomorphic monoidal closed structures. This severely contrasts with the situation concerning symmetric monoidal closed structures, because it is shown in [13] that PRAP only admits one symmetric tensorproduct, up to natural isomorphism.
      758  648
  • Publication
    A Connected, not Separably Connected Metric Space
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2001)
    Simon, Petr
    A separably connected space is a topological space, where every two points may be joined by a separable connected subspace. We present an example of a connected, but not separably connected metric space and of a connected metric space, which contains no connected separable subspaces other than one-point ones.
      1201  1222
  • Publication
    The Cartesian Closed Topological Hull of the Category of (Quasi-)Uniform Spaces (Revisited)
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2001)
    Nauwelaerts, Mark
    This paper provides a concrete description of the cartesian closed topological hull of qUnif, the category of quasi-uniform spaces and uniformly continuous maps, inside q(S)ULim, the category of quasi-(semi-)uniform limit spaces and uniformly continuous maps, which also allows to derive a similar and new description of the CCT hull of Unif inside (S)ULim. In both cases, the objects of the CCT hull are (quasi-)(semi-)uniform limit spaces whose collection of filters satisfies some natural closure condition, related to the (q)Unif-bireflection of the space in question.
      909  1023
  • Publication
    The Concept of Separable Connectedness: Applications to General Utility Theory
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2001)
    Induráin, Esteban
    We say that a topological set X is separably connected if for any two points $x,\; y\;\epsilon\; X$ there exists a connected and separable subset $C\left(x,y\right)\subseteq X$ to which both x and y belong. This concept generalizes path-connectedness. With this concept we have improved some results on general utility theory: For instance, in 1987 Monteiro gave conditions (dealing with real-valued, continuous, order-preserving functions) on path-connected spaces in order to get continuous utility representations of continuous total preorders defi{}ned on the set. We have recently proved (in an article by Candeal, Hervès and Indurain, published in the Journal of Mathematical Economics, 1998) that Monteiro\textquoteright{}s results also work for the more general case of separably connected spaces. Then we study the particular situation of separable connectedness on spaces endowed with some extra structure, e.g. metric spaces.
      935  1409