On the density and net weight of regular spaces
Volume 107 / 2007
Colloquium Mathematicum 107 (2007), 267-272
MSC: Primary 54A25.
DOI: 10.4064/cm107-2-6
Abstract
We use the cardinal functions $ac$ and $lc$, due to Fedeli, to establish bounds on the density and net weight of regular spaces which improve some well known bounds. In particular, we use the language of elementary submodels to establish that $d(X)\leq \pi \chi (X)^{ac(X)}$ for every regular space $X$. This generalizes the following result due to Shapirovskiĭ: $d(X)\leq \pi \chi (X)^{c(X)}$ for every regular space $X$.
