Geodesic
Class of topologies in spaces of continuous functions
Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 201-208

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Let $S$ be an arbitrary topological space, and let $C(S)$ be the space of continuous real-valued functions on $S$. A certain class of topologies on $C(S)$ is studied. Some cases are indicated in which topologies of a given class on $C(S)$ are topologies of uniform convergence on compact sets of $S$. 
@article{MZM_1972_11_2_a9,
     author = {I. I. Perepechai},
     title = {Class of topologies in spaces of continuous functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {201--208},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a9/}
}
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I. I. Perepechai. Class of topologies in spaces of continuous functions. Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 201-208. http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a9/