Indestructibly productively Lindelöf and Menger function spaces

Abstract

For a Tychonoff space $X$ and a family $\lambda$ of subsets of $X$, we denote by $C_{\lambda }(X)$ the $T_1$-space of all real-valued continuous functions on $X$ with the $\lambda$ -open topology. A topological space is productively Lindelöf if its product with every Lindelöf space is Lindelöf. A space is indestructibly productively Lindelöf if it is productively Lindelöf in any extension by countably closed forcing. In this paper, we study indestructibly productively Lindelöf and Menger function space $C_{\lambda }(X)$.

12 pages