### Cellularity and the index of narrowness in topological groups

Mihail G. Tkachenko (2011)

Commentationes Mathematicae Universitatis Carolinae

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We study relations between the cellularity and index of narrowness in topological groups and their ${G}_{\delta}$-modifications. We show, in particular, that the inequalities $in\left({\left(H\right)}_{\tau}\right)\le {2}^{\tau \xb7in\left(H\right)}$ and $c\left({\left(H\right)}_{\tau}\right)\le {2}^{{2}^{\tau \xb7in\left(H\right)}}$ hold for every topological group $H$ and every cardinal $\tau \ge \omega $, where ${\left(H\right)}_{\tau}$ denotes the underlying group $H$ endowed with the ${G}_{\tau}$-modification of the original topology of $H$ and $in\left(H\right)$ is the index of narrowness of the group $H$. Also, we find some bounds for the complexity of continuous real-valued functions $f$ on an arbitrary $\omega $-narrow group...