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• W1833150493 abstract "Many classically used function space structures (including the topology of pointwise convergence, the compact-open topology, the Isbell topology and the continuous convergence) are induced by a hyperspace structure counterpart. This scheme is used to study local properties of function space structures on $C(X,mathbb R)$, such as character, tighntess, fan-tightness, strong fan-tightness, the Fr{e}chet property and some of its variants. Under mild conditions, local properties of $C(X,mathbb R)$ at the zero function correspond to the same property of the associated hyperspace structure at $X$. The latter is often easy to characterize in terms of covering properties of $X$. This way, many classical results are recovered or refined, and new results are obtained. In particular, it is shown that tightness and character coincide for the continuous convergence on $C(X,mathbb R)$ and is equal to the Lindel{o}f degree of $X$. As a consequence, if $X$ is consonant, the tightness of $C(X,mathbb R)$ for the compact-open topology is equal to the Lindel{o}f degree of $X$." @default.
• W1833150493 created "2016-06-24" @default.
• W1833150493 creator A5013236555 @default.
• W1833150493 creator A5055452635 @default.
• W1833150493 date "2010-02-15" @default.
• W1833150493 modified "2023-09-27" @default.
• W1833150493 title "A unified theory of function spaces and hyperspaces: local properties" @default.
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• W1833150493 hasPublicationYear "2010" @default.
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