The quasi Isbell topology on function spaces
Volume 141 / 2015
Colloquium Mathematicum 141 (2015), 13-24
MSC: Primary 54C35.
DOI: 10.4064/cm141-1-2
Abstract
In this paper, on the family ${\mathcal O}(Y)$ of all open subsets of a space $Y$ we define the so called quasi Scott topology, denoted by $\tau _{\rm qSc}$. 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 $t_{\rm qIs}$ 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 $t_{\rm qIs}$ are given.
