Properties of the $C$-compact-open topology on a function space

A. V. Osipov

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 258-277

Résumé

We study the $C$-compact-open topology on the set $C(X)$ of all continuous real-valued functions defined on a Tikhonov space $X$. The relations between the $C$-compact-open topology and the compact-open and bounded-open topologies on the set $X$ are studied. We also investigate the cardinal-valued characteristics of the space $C(X)$ equipped with the $C$-compact-open topology, for example, the Suslin number, Lindelöf number, weight, and density.

Détail

Keywords: space of continuous functions, set-open topology, compact-open topology, $C$-compact subset, topology of uniform convergence.

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