Geodesic
Compacta lying in the $n$-dimensional universal Menger compactum and
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 471-484

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The concept of $n$-shape is defined for an arbitrary compactum, and it is proved that two $Z$-sets lying in the $(n+1)$-dimensional universal Menger compactum have homeomorphic complements in it precisely when their $n$-shapes are equal. Bibliography: 15 titles. 
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     author = {A. Ch. Chigogidze},
     title = {Compacta lying in the $n$-dimensional universal {Menger} compactum and},
     journal = {Sbornik. Mathematics},
     pages = {471--484},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_2_a12/}
}
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A. Ch. Chigogidze. Compacta lying in the $n$-dimensional universal Menger compactum and. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 471-484. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a12/