Geodesic
On a countable base and the conjugate class of a topological space
Sbornik. Mathematics, Tome 29 (1976) no. 1, pp. 13-33 
P. L. Ul'yanov. On a countable base and the conjugate class of a topological space. Sbornik. Mathematics, Tome 29 (1976) no. 1, pp. 13-33. http://geodesic.mathdoc.fr/item/SM_1976_29_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the classes $\varphi (L)$ of functions are studied, and the topological spaces $U_\varphi$ are constructed from them. In particular, a necessary and sufficient condition guaranteeing a countable base in $U_\varphi$ is found. Classes $\overline\varphi (L)$ of functions conjugate (relative to sum) to $\varphi (L)$ are introduced and investigated. Bibliography: 7 titles.

[1] Dzh. L. Kelli, Obschaya topologiya, izd-vo «Nauka», Moskva, 1968

[2] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, izd-vo «Nauka», Moskva, 1968 | MR

[3] P. L. Ulyanov, “O nekotorykh approksimativnykh i topologicheskikh svoistvakh prostranstva funktsii $\varphi(L)$”, DAN SSSR, 203:3 (1972), 534–536

[4] P. L. Ulyanov, “Predstavlenie funktsii ryadami i klassy $\varphi(L)$”, Uspekhi matem. nauk, XXVII:2 (164) (1972), 3–52 | MR

[5] P. L. Ulyanov, “O nekotorykh svoistvakh prostranstva funktsii $\varphi(L)$”, DAN SSSR, 216:2 (1974), 278–281

[6] P. L. Ulyanov, “O razlichnykh vidakh skhodimosti v klassakh $\varphi(L)$”, Trudy Matem. in-ta im. V. A. Steklova, CXXXIV (1975), 327–352

[7] I. P. Natanson, Teoriya funktsii veschestvennoi peremennoi, Gostekhizdat, Moskva, 1957 | MR