The quasi Isbell topology on function spaces

D. N. Georgiou ¹   ; A. C. Megaritis ²

¹ Department of Mathematics University of Patras 265 04 Patras, Greece
² Department of Accounting and Finance Technological Educational Institute of Western Greece 302 00 Messolonghi, Greece

Colloquium Mathematicum, Tome 141 (2015) no. 1, pp. 13-24

Résumé

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.

Détail

DOI : 10.4064/cm141-1-2

Keywords: paper family mathcal subsets space define called quasi scott topology denoted tau qsc topology defines standard set continuous maps space space nbsp topology qis called quasi isbell topology latter topology always larger equal isbell topology smaller equal strong isbell topology results problems concerning topology qis given