Characterizations of some topologies on function spaces
by
D. N. Georgiou
University of Thessaly, Volos, Greece
Coauthors: S. Iliadis, B. K. Papadopoulos

Let X, Y and Z be topological spaces. A mapping F:X×Y --> Z is said to be coordinately continuous if for every x in X (respectively, y in Y) the restriction of F onto the set {x}×X (respectively, {y}×Y) is continuous.

If in the definition of the splitting and jointly continuous topologies we replace the continuity of mapping (of the product spaces) by the coordinately continuous we obtain variations of splittingness and jointly continuity (about difference such variations see [1] and [2]).

These variations of splittingness and jointly continuity are used to study some topologies on function spaces.

References

[1] D. N. Georgiou, S. D. Iliadis and B. Papadopoulos, Topologies on function spaces, Studies in Topology, VII, Zapiski Nauchnykh Seminarov S.-Peterburg Otdel. Mat. Inst. Steklov (POMI), (210) 1992, pp. 82-97. J. Math. Sci., New York 81, (1996), No. 2, pp. 2506-2514.

[2] A. A. Ivanov, Bitopologies of products and ratios, Fundamentalnya i prikladnaya matematika Vol. 4 (1998), No.1, p.119-125.

Date received: June 23, 2000