Short notes

The Lindelöff number functional spaces over monolithic compacta

D. P. Baturov^a, E. A. Reznichenko<sup>b

a</sup> Orel State University
^b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

UDC: 515.12

Received: 14.12.2016

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2018, 73:3, 116–119

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