In this paper, on the family (Y) of all open subsets of a space Y we define the so called quasi Scott topology, denoted by . This topology defines in a standard way, on the set C(Y,Z) of all continuous maps of the space Y to a space Z, a topology called the quasi Isbell topology. The latter topology is always larger than or equal to the Isbell topology, and smaller than or equal to the strong Isbell topology. Results and problems concerning the topology are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-2,
author = {D. N. Georgiou and A. C. Megaritis},
title = {The quasi Isbell topology on function spaces},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {13-24},
zbl = {1328.54012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-2}
}
D. N. Georgiou; A. C. Megaritis. The quasi Isbell topology on function spaces. Colloquium Mathematicae, Tome 139 (2015) pp. 13-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-2/