Kurt Gödel Research Center

2012 seminar talk: Set-open topology on the space of continuous functions

Talk held by Alexander Osipov (Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Russia) at the KGRC seminar on 2012-05-10.

Abstract

For a Tychonoff space $X$, we denote by $C_{\lambda}(X)$ the space of all real-valued continuous functions on $X$ with set-open topology.

We investigate the topological-algebraic properties of $C_{\lambda}(X)$ such as submetrizability, metrizability, separability and other. We also compare this topology with several well-known and lesser known topologies (for example, topology of uniform convergence).