The quasi Isbell topology on function spaces

Tom 141 / 2015

D. N. Georgiou, A. C. Megaritis Colloquium Mathematicum 141 (2015), 13-24 MSC: Primary 54C35. DOI: 10.4064/cm141-1-2


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.


  • D. N. GeorgiouDepartment of Mathematics
    University of Patras
    265 04 Patras, Greece
  • A. C. MegaritisDepartment of Accounting and Finance
    Technological Educational Institute
    of Western Greece
    302 00 Messolonghi, Greece

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