Topologies on function spaces and hyperspaces

D. N. Georgiou


Let Y and Z be two fixed topological spaces, O(Z) the family of all open subsets of Z, C(Y,Z) the set of all continuous maps from Y to Z, and OZ(Y ) the set {f−1(U) : f ϵ C(Y,Z) and U ϵ O(Z)}. In this paper, we give and study new topologies on the sets C(Y,Z) and OZ(Y ) calling (A,A0)-splitting and (A,A0)-admissible, where A and A0 families of spaces.


Space; Hyperspace; Splitting topology; Admissible topology

Full Text:



R. Arens, A topology of spaces of transformations, Annals of Math. 47 (1946), 480-495.

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

J. Dugundji, Topology, Allyn and Bacon, Inc. Boston 1968.

G. Di Maio, L. Holá, D. Hol'y and R. McCoy, Topologies on the set space of continuous functions, Topology Appl. 86 (1998), no. 2, 105-122.

G. Di Maio, E. Meccariello and S. Naimpally, Hyper-continuous convergence in function spaces, Quest. Answers Gen. Topology 22 (2004), no. 2, 157-162.

R. Engelking, General Topology, Warszawa 1977.

R. H. Fox, On topologies for function spaces, Bull. Amer. Math. Soc. 51 (1945), 429-432.

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 (Russian). Translated in: J. Math. Sci., New York 81, (1996), no. 2, 2506-2514.

D. N. Georgiou, S. D. Iliadis and B. K. Papadopoulos, On dual topologies, Topology Appl. 140 (2004), 57-68.

D. N. Georgiou, S.D. Iliadis and F. Mynard, Function space topologies, Open Problems in Topology 2 (Elsevier), 15-23, 2007.

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.

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.

R. McCoy and I. Ntantu, Topological properties of spaces of continuous functions, Lecture Notes in Mathematics, 1315, Springer Verlang.

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.

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM


Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. On cofree S-spaces and cofree S-flows
Behnam Khosravi
Applied General Topology  vol: 13  issue: 1  year: 2013  
doi: 10.4995/agt.2012.1632

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147