n-Tuple relations and topologies on function spaces
Keywords:Function space, A-splitting topology, A-jointly continuous topology
In some results concerning S-splitting, S-jointly continuous, D-splitting and D-jointly continuous topologies are considered, where S and D are the Sierpinski space and the double-point space, respectively. Here we generalize these results replacing the spaces S and D by any finite space.
R. Arens, A topology of spaces of transformations, Annals of Math., 47(1946), 480-495. https://doi.org/10.2307/1969087
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 1968).
P. Fletcher and W. Lindgren, Quasi-uniform spaces, (Lecture Notes in Pure and Applied Mathematics; Vol. 77 (1982)).
R. H. Fox, On topologies for function spaces, Bull. Amer. Math. Soc. 51(1945), 429-432. https://doi.org/10.1090/S0002-9904-1945-08370-0
D. N. Georgiou, S.D. Iliadis and B. K. Papadopoulos, Topologies on function spaces, Studies in Topology, VII, Zap. Nauchn. Sem. S.-Peterburg Otdel. Mat. Inst. Steklov (POMI), 208(1992), 82-97. J. Math. Sci., New York 81(1996), No. 2, 2506-2514. https://doi.org/10.1007/BF02362419
D. N. Georgiou, S.D. Iliadis and B. K. Papadopoulos, Topologies and orders on function spaces, Publ. Math. Debrecen, 46/ 1-2 (1995), 1-10.
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 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).
M. G. Murdershwar and S. A. Naimpaly, Quasi uniform spaces, (Noordhoff, 1966).
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.