Baire category properties of function spaces with the Fell hypograph topology

Abstract

For a Tychonoff space $X$ and a subspace $Y\subset \mathbb{R}$, we study Baire category properties of the space $C_{\downarrow F}(X,Y)$ of continuous functions from $X$ to $Y$, endowed with the Fell hypograph topology. We characterize pairs $X,Y$ for which the function space $C_{\downarrow F}(X,Y)$ is $\infty$-meager, meager, Baire, Choquet, strong Choquet, (almost) complete-metrizable or (almost) Polish.

35 pages

References in corpus (1)

• On Baire category properties of function spaces $C_k^{\prime }(X,Y)$

Cited by in corpus (2)

• On Baire category properties of function spaces $C_k^{\prime }(X,Y)$
• Lusin and Suslin properties of function spaces