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Compacta lying in the $n$-dimensional universal Menger compactum and having homeomorphic complements in it

A. Ch. Chigogidze


Abstract: 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.

UDC: 515.12

MSC: Primary 54C56, 55P55; Secondary 54D05, 54G05

Received: 12.06.1986

 English version: Mathematics of the USSR-Sbornik, 1988, 61:2, 471–484

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