1. CMB 2012 (vol 57 pp. 61)
 Geschke, Stefan

2dimensional Convexity Numbers and $P_4$free Graphs
For $S\subseteq\mathbb R^n$ a set
$C\subseteq S$ is an $m$clique if the convex hull of no $m$element subset of
$C$ is contained in $S$.
We show that there is essentially just one way to construct
a closed set $S\subseteq\mathbb R^2$ without an uncountable
$3$clique that is not the union of countably many convex sets.
In particular, all such sets have the same convexity number;
that is, they
require the same number of convex subsets to cover them.
The main result follows from an analysis of the convex structure of closed
sets in $\mathbb R^2$ without uncountable 3cliques in terms of
clopen, $P_4$free graphs on Polish spaces.
Keywords:convex cover, convexity number, continuous coloring, perfect graph, cograph Categories:52A10, 03E17, 03E75 

2. CMB 2010 (vol 53 pp. 286)
 Gorelic, Isaac

Orders of πBases
We extend the scope of B. Shapirovskii's results on the order of $\pi$bases in compact spaces and answer some questions of V. Tkachuk.
Keywords:Shapirovskii πbase, pointcountable πbase, free sequences, canonical form for ordinals Categories:54A25, 03E10, 03E75, 54A35 
