For a non-empty set X
and a given family **F** of subsets of X such that **F** does not contain
the empty set, we
consider the Marczewski field
S(**F**) which consists of subsets A of X such that each set
U in **F** contains a set V in **F** with
such that V is either disjoint with of contained in A.
We also study the respective ideal S^{0}(**F**).
We show general properties of S(**F**) and certain representation theorems.
For instance we prove that the interval algebra in [0,1) is a
Marczewski field. We are also interested in
situations where S(**F**)=S(\tau \ {emptyset}) for a topology
\tau on X.
We propose a general method which establishes S(**F**) and
S^{0}(**F**) provided that
**F** is the family of perfect sets with respect to \tau, and \tau is
a certain ideal topology on **R** connected with measure or category.

**Last modified December 16, 2000.**