A note on locally v-bounded spaces

• Georgiou, D.N. ^[1] ; Iliadis, S.D. ^[1]
  1. [1] University of Patras

     University of Patras

     Dimos Patras, Grecia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 6, Nº. 2, 2005, págs. 143-148
• Idioma: inglés
• DOI: 10.4995/agt.2005.1953
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• Resumen

  • In this paper, on the family O(Y ) of all open subsets of a space Y (actually on a complete lattice) we define the so called strong v-Scott topology, denoted by τ8v,  where v is an infinite cardinal. This topology defines on the set C(Y,Z) of all continuous functions on the space Y to a space Z a topology τ8v. The topology τ8v, is always larger than or equal to the strong Isbell topology. We study the topology τ8v in the case where Y is a locally v-bounded space.

• Referencias bibliográficas
  • R. Arens and J. Dugundji, Topologies for function spaces, Pacific J. Math. 1(1951), 5-31. http://dx.doi.org/10.2140/pjm.1951.1.5
  • J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass. 1966.
  • S. Gagola and M. Gemignani, Absolutely bounded sets, Mathematica Japonicae, Vol. 13, No. 2 (1968), 129-132.
  • D. N. Georgiou and S. D. Iliadis, A generalization of core compact spaces, (V Iberoamerican Conference of Topology and its Applications) Topology...
  • G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, A Compendium of Continuous Lattices, Springer, Berlin-Heidelberg-New...
  • P. Lambrinos, Subsets (m, n)-bounded in a topological space, Mathematica Balkanica, 4(1974), 391-397.
  • P. Lambrinos, Locally bounded spaces, Proceedings of the Edinburgh Mathematical Society, Vol. 19 (Series II) (1975), 321-325.
  • P. Lambrinos and B. K. Papadopoulos, The (strong) Isbell topology and (weakly) continuous lattices, Continuous Lattices and Applications,...
  • R. McCoy and I. Ntantu, Topological properties of spaces of continuous functions, Lecture Notes in Mathematics, 1315, Springer Verlang (1988).
  • H. Poppe, On locally defined topological notions, Q and A in General Topology, Vol. 13 (1995), 39-53.
  • F. Schwarz and S. Weck, Scott topology, Isbell topology and continuous convergence, Lecture Notes in Pure and Appl. Math. No. 101, Marcel...