arXiv subjects

Dimitris Georgiou

Publications and source records attributed to Dimitris Georgiou.

2 recordsLinked to original sources

arXiv2018

A study concerning splitting and jointly continuous topologies on $C(Y,Z)$

Let $Y$ and $Z$ be two fixed topological spaces and $C(Y,Z)$ the set of all continuous maps from $Y$ into $Z$. We construct and study topologies on $C(Y,Z)$ that we call ${\cal F}_n(τ_n)$-family-open topologies. Furthermore, we find necessary and sufficient conditions such that these topologies to be splitting and jointly continuous. Finally, we present questions concerning a further study on this area.

math.GN↗

arXiv2017

Admissible topologies on $C(Y,Z)$ and ${\cal O}_Z(Y)$

Let $Y$ and $Z$ be two given topological spaces, ${\cal O}(Y)$ (respectively, ${\cal O}(Z)$) the set of all open subsets of $Y$ (respectively, $Z$), and $C(Y,Z)$ the set of all continuous maps from $Y$ to $Z$. We study Scott type topologies on ${\mathcal O}(Y)$ and we construct admissible topologies on $C(Y,Z)$ and ${\mathcal O}_Z(Y)=\{f^{-1}(U)\in {\mathcal O}(Y): f\in C(Y,Z)\ {\rm and}\ U\in {\mathcal O}(Z)\}$, introducing new problems in the field.

math.GN↗