Geodesic
On the coincidence of the set-open and uniform topologies
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 177-184

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The $\mathbb R$-compactness property is studied and criteria are established for the coincidence of the set-open topology and the topology of uniform convergence on the spaces of continuous functions.
Keywords: space of continuous functions, set-open topology, topology of uniform convergence on a family of sets. 
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S. È. Nokhrin; A. V. Osipov. On the coincidence of the set-open and uniform topologies. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 177-184. http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a15/