http://www.openstarts.units.it:80/dspace/handle/10077/4280 2013-05-24T14:04:16Z http://www.openstarts.units.it:80/dspace/handle/10077/4294 Title: On Hyperbolic 3-Orbifolds of Small Volume and Small Heegaard Genus Authors: Zimmermann, Bruno Abstract: 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]. Type: Articolo 2001-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4293 Title: How Many Closed Structures does the Construct PRAP Admit? Authors: Sioen, Mark Abstract: 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. Type: Articolo 2001-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4292 Title: A Connected, not Separably Connected Metric Space Authors: Simon, Petr Abstract: 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. Type: Articolo 2001-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4291 Title: The Cartesian Closed Topological Hull of the Category of (Quasi-)Uniform Spaces (Revisited) Authors: Nauwelaerts, Mark Abstract: 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. Type: Articolo 2001-01-01T00:00:00Z