THE BOREL STRUCTURE OF THE COLLECTIONS OF SUB-SELF-SIMILAR SETS AND SUPER-SELF-SIMILAR SETS
Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 2
M. Mcclure; R. W. Vallin. THE BOREL STRUCTURE OF THE COLLECTIONS OF SUB-SELF-SIMILAR SETS AND SUPER-SELF-SIMILAR SETS. Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2000_69_2_a1/
@article{AMUC_2000_69_2_a1,
     author = {M. Mcclure and R. W. Vallin},
     title = {THE {BOREL} {STRUCTURE} {OF} {THE} {COLLECTIONS} {OF} {SUB-SELF-SIMILAR} {SETS} {AND} {SUPER-SELF-SIMILAR} {SETS}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2000},
     volume = {69},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2000_69_2_a1/}
}
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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.