Geodesic
On properties of infimal topology of a~map space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 87-99

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We study properties of the infimal topology $\tau_\mathrm{inf}$ which is the infimum of the family of all topologies of uniform convergence defined on the set $C(X,Y)$ of continuous maps into a metrizable space $Y$. One of the main results of the research consists in obtaining necessary and sufficient condition for the topology $\tau_\mathrm{inf}$ to have the Fréchet–Urysohn property. We also establish necessary and sufficient conditions for coincidence of the topology $\tau_\mathrm{inf}$ and a topology of uniform convergence $\tau_\mu$.
Keywords: map space, topology of uniform convergence, infimal topology. 
@article{IVM_2016_4_a10,
     author = {V. L. Timokhovich and D. S. Frolova},
     title = {On properties of infimal topology of a~map space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {87--99},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_4_a10/}
}
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V. L. Timokhovich; D. S. Frolova. On properties of infimal topology of a~map space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 87-99. http://geodesic.mathdoc.fr/item/IVM_2016_4_a10/