Geodesic
Topologies of uniform convergence. The property in the sense of Arens--Dugundji and the sequential property
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2013), pp. 45-58.

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This contribution investigates the properties of the topologies $\tau_\mathrm{sup}$ and $\tau_\mathrm{inf}$, which are, respectively, the supremum and the infimum of the family of all topologies of uniform convergence defined on the set $C(X,Y)$ of continuous maps into metrizable space $Y$. The main result of the research are necessary and sufficient conditions for properness and admissibility in the terms of Arens-Dugundji obtained for the topology $\tau_\mathrm{inf}$. The article introduces the notion of sequentially proper topology and establishes necessary and sufficient conditions for sequential properness of the topology $\tau_\mathrm{inf}$. It also considers a special case when the greatest proper topology and the greatest sequentially proper topology coincide on the set $C(X,Y)$.
Keywords: mapping space, topology of uniform convergence, admissible topology, proper topology, sequentially proper topology. 
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V. L. Timokhovich; D. S. Frolova. Topologies of uniform convergence. The property in the sense of Arens--Dugundji and the sequential property. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2013), pp. 45-58. http://geodesic.mathdoc.fr/item/IVM_2013_9_a5/

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