Developable hyperspaces are metrizable

• Holá, L'Ubica ^[2] ; Pelant, Jan ^[3] ; Zsilinszky, László ^[1]
  1. [1] University of North Carolina at Pembroke

     University of North Carolina at Pembroke

     Township of Pembroke, Estados Unidos

     
  2. [2] Academy of Sciences
  3. [3] Czech Academy of Sciences

  Mostrar afiliaciones +
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 4, Nº. 2, 2003, págs. 351-360
• Idioma: inglés
• DOI: 10.4995/agt.2003.2038
• Enlaces
  • Texto completo
• Resumen

  • Developability of hyperspace topologies (locally finite, (bounded) Vietoris, Fell, respectively) on the nonempty closed sets is characterized. Submetrizability and having a Gδ-diagonal in the hyperspace setting is also discussed.

• Referencias bibliográficas
  • H. Attouch, Variational convergence for functions and operators, Pitman, Boston (1984).
  • G. Beer, Topologies on Closed and Closed Convex Sets, Kluwer, Dordrecht (1993).
  • G. Beer, On the Fell Topology, Set-Valued Anal.1 (1993), 69-80. http://dx.doi.org/10.1007/BF01039292
  • G. A. Beer, C. J. Himmelberg, K. Prikry and F. S. Van Vleck, The locally finite topology on 2X, Proc. Amer. Math. Soc.101 (1987), 168-172....
  • G. Beer, A. Lechicki, S. Levi and S. Naimpally, Distance functionals and suprema of hyperspace topologies, Ann. Mat. Pura Appl. (4) 162 (1992),...
  • H. Brandsma, Monolithic Hyperspaces; PhD. Thesis, Vrije Universiteit, Amsterdam (1998).
  • H. Brandsma and J. van Mill, Monotonically normal hyperspaces are metrisable.
  • M. Coban, Note sur topologie exponentielle, Fundam. Math.71 (1971), 27-42.
  • G. Di Maio, L'. Holá and J. Pelant, Properties related to the first countability of hyperspace topologies, Questions and Answers in General...
  • G. Di Miao and L'. Holá, On hit-and-miss topologies, Rend. Acc. Sc. Fis. Mat. Napoli 62 (1995), 103-124.
  • R. Engelking, General Topology, Helderman, Berlin (1989).
  • V. V. Fedorchuk, On some geometric properties of functors, Rend. Circ. Mat. Palermo (2) Suppl. 24 (1990), 73-78.
  • S. Fisher, P. Gartside, T. Mizokami and N. Shimane, Near metric properties of hyperspaces, Topol. Proc. 22 (1997), 197-211 .
  • S. L. Gulden, W. M. Fleischman and J. H. Weston, Linearly Ordered Topological Spaces, Proc. Amer. Math. Soc. 24 (1970), 760-766. http://dx.doi.org/10.1090/S0002-9939-1970-0253292-7
  • G. Gruenhage, Generalized metric spaces, in Handbook of Set-Theoretic topology edited by K. Kunen and J. Vaughan (1984), 423-501.
  • L'. Holá and S. Levi, Decomposition Properties of Hyperspace Topologies, Set-Valued Anal. 5 (1997), 309-321. http://dx.doi.org/10.1023/A:1008608209952
  • L'. Holá, S. Levi and J. Pelant, Normality and paracompactnees of the Fell topology, Proc. Amer. Math. Soc. 127 (1999), 2193-2197. http://dx.doi.org/10.1090/S0002-9939-99-04737-1
  • L'. Holá and H.P. Künzi, Properties related to compactness in hyperspaces, Topology Proceedings 23 (1998), 191-205.
  • J. Keesling, Normality and properties related to compactness in hyperspaces, Proc. Amer. Math. Soc. 24 (1970), 760-766. http://dx.doi.org/10.1090/S0002-9939-1970-0253292-7
  • J. Keesling, On the equivalence of normality and compactness in hyperspaces, Pacific J. Math. 33 (1970), 657-667. http://dx.doi.org/10.2140/pjm.1970.33.657
  • G. Matheron, Random sets and integral geometry, Wiley, New York (1975)
  • E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182. http://dx.doi.org/10.1090/S0002-9947-1951-0042109-4
  • T. Mizokami, Hyperspaces of a Moore space and a d-paracompact space, Glas. Mat. 30 (1995), 69-72.
  • T. Mizokami, On hyperspaces of spaces around Moore spaces, Houston J. Math. 22 (1996), 297-306 .
  • S. A. Naimpally and P. L. Sharma, Fine uniformity and the locally finite hyperspace topology, Proc. Amer. Math. Soc. 103 (1988), 641-646....
  • V. Popov, On the subspaces of expX, in: Colloquia Mathematica, Soc. J. B_olyai, Budapest 103 (1978), 977-984.
  • N. V. Velichko, On spaces of closed subsets, Sib. Math. J. 16 (1975), 484-486. http://dx.doi.org/10.1007/BF00967540
  • L. Zsilinszky, Topological games and hyperspace topologies, Set-Valued Anal. 6 (1998), 187- 207 . http://dx.doi.org/10.1023/A:1008669420995