looking for Theorem 3.22 of Cardinal functions in topology

Question

read an article which uses Theorem 3.22 of "Cardinal functions in topology, ten years later". I searched this book on internet but is not there. I searched it in my university library but isn't there either. Does any body know that it says this theorem? Than you!

Answer 1

I seem to recall a .pdf of this book being available from István Juhász's web site, but the "publications" link doesn't appear to be working right now.

Anyway, here is the statement:

If $\beta \mathbb{N}$ does not embed into a compact Hausdorff space $X$, then $\rho ( X ) \leq 2^{c(X)}$

where

• $\rho(X) = | \{ U \subseteq X : U\text{ is regular open} \} |$;
• $c(X) = \sup \{ |\mathcal{U}| : \mathcal{U}\text{ is a family of pairwise disjoint open subsets of }X \} + \omega$ is the cellularity of $X$.

Answer 2

For the record, this is Math. Centre Tracts $123$. It is available as a PDF from the Institutional Digital Repository of CWI (Centrum Wiskunde & Informatica). The search page is here; the easiest search is to use the dropdown box for the Name field. A direct link to the PDF is here.