Geodesic
The Lindelöff number functional spaces over monolithic compacta
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 57-60 
D. P. Baturov; E. A. Reznichenko. The Lindelöff number functional spaces over monolithic compacta. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 57-60. http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a8/
@article{VMUMM_2018_3_a8,
     author = {D. P. Baturov and E. A. Reznichenko},
     title = {The {Lindel\"off} number functional spaces over monolithic compacta},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {57--60},
     year = {2018},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a8/}
}
TY  - JOUR
AU  - D. P. Baturov
AU  - E. A. Reznichenko
TI  - The Lindelöff number functional spaces over monolithic compacta
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2018
SP  - 57
EP  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a8/
LA  - ru
ID  - VMUMM_2018_3_a8
ER  - 
%0 Journal Article
%A D. P. Baturov
%A E. A. Reznichenko
%T The Lindelöff number functional spaces over monolithic compacta
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2018
%P 57-60
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a8/
%G ru
%F VMUMM_2018_3_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X$ be a compactum, $\tau$ be an infinite cardinal, and $t(X)\le\tau$. In this case, $l(C_p(X))\le 2^\tau$. If $X$ is $\tau$-monolithic, then $l(C_p(X))\le \tau^+$. In addition, if $X$ is zero-dimensional and there are no $\tau ^+$-Aronszajn trees, then $l(C_p(X))\le \tau$.

[1] Arkhangelskii A.V., Topologicheskie prostranstva funktsii, Izd-vo MGU, M., 1989 | MR

[2] Kyunen K., “Kombinatorika”, Spravochnaya kniga po matematicheskoi logike, v. II, Teoriya mnozhestv, ed. Dzh. Barvais, Nauka, M., 1982, 64–98

[3] Engelking R., Obschaya topologiya, Mir, M., 1986 | MR

[4] Okunev O., Reznichenko E., “A note on surlindelöf spaces”, Topology Proceedings, 31:2 (2007), 667–675 | MR | Zbl

[5] Todorčević S., “Trees and linearly ordered sets”, Handbook of Set-Theoretic Topology, eds. K. Kunen, J. E. Vaughan, North-Holland, Amsterdam, 1984, 235–294 | MR