ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 69,   2   (2000)
pp.   145-149

THE BOREL STRUCTURE OF THE COLLECTIONS OF SUB-SELF-SIMILAR SETS AND SUPER-SELF-SIMILAR SETS
M. MCCLURE and R. W. VALLIN

Abstract.  We show that the sets of \su sets and \Su sets are both dense, first category, $F_\sigma$ subsets of $\Cal K(\rd)$, the Hausdorff metric space of non-empty compact, subsets of $\rd$. We also investigate the set of \se sets as a subset of the \su sets and the \Su sets.

AMS subject classification.  54B20
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