The Lindelöf Number of Functional Spaces on Monolithic Compacta / D. P. Baturov and E. A. Reznichenko. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. № 3. P. 57-60 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 116-119].

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 .

Key words: function space, Lindelöf number, tightness, monolithic compactum, Aronszajn tree.

№ 3/2018