For an algebra **A** and an ideal **I** of subsets of a set X we consider pairs
(**A**,**I**) which have the common inner Marczewski-Burstin
representation. The main goal of the paper is to
investigate which inner Marczewski-Burstin representable algebras and pairs are topological.

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**See also Errata ( Real Anal. Exchange 29(2) (2003-2004), 7-8)
in pdf,
postscript,
and LaTeX
2e formats. **

**Last modified May 26, 2004.**