A note on locally v-bounded spaces

Authors

  • D. N. Georgiou University of Patras
  • Stavros Iliadis University of Patras

DOI:

https://doi.org/10.4995/agt.2005.1953

Keywords:

Strong Scott topology, Strong Isbell topology, Function space, Admissible topology

Abstract

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.

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Author Biographies

D. N. Georgiou, University of Patras

Department of Mathematics

Stavros Iliadis, University of Patras

Department of Mathematics

References

R. Arens and J. Dugundji, Topologies for function spaces, Pacific J. Math. 1(1951), 5-31. https://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 and its Applications.

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 York 1980. https://doi.org/10.1007/978-3-642-67678-9

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. https://doi.org/10.1017/S0013091500010415

P. Lambrinos and B. K. Papadopoulos, The (strong) Isbell topology and (weakly) continuous lattices, Continuous Lattices and Applications, Lecture Notes in Pure and Appl. Math. No. 101, Marcel Dekker, New York 1984, 191-211. https://doi.org/10.1201/9781003072621-11

R. McCoy and I. Ntantu, Topological properties of spaces of continuous functions, Lecture Notes in Mathematics, 1315, Springer Verlang (1988). https://doi.org/10.1007/BFb0098389

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 Dekker, New York 1984, 251-271. https://doi.org/10.1201/9781003072621-15

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How to Cite

[1]
D. N. Georgiou and S. Iliadis, “A note on locally v-bounded spaces”, Appl. Gen. Topol., vol. 6, no. 2, pp. 143–148, Oct. 2005.

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