Partition properties of homogeneous relational structures are determined by
their automorphism groups. Hence permutation groups closed in the finitary
topology have partition properties, lifted from the partiton properties of the
underlying homogeneous structures. Those properties can be defined using
permutation group notions only. On the other hand due to results of
Kechris, Pestov and Todorcevic and Pestov various connections between actions
of topological groups on compacta and relational Ramsey theory have become
known.

In order to illustrate various of those partition properties and their
interrelationships the simpler case of point partitions will be discussed.