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Inductive dimension of subsets of some nonmetrizable manifolds. (English. Russian original) Zbl 0909.54029
Mosc. Univ. Math. Bull. 52, No. 5, 11-13 (1997); translation from Vestn. Mosk. Univ., Ser. I 1997, No. 5, 11-14 (1997).
The paper deals with the closed subsets of nonmetrizable manifolds of the form \(M^n\times L\), where \(M^n\) is a compact \(n\)-manifold, \(L\) is a “long” Aleksandrov straight line. It is proved that:
(a) for any closed subset \(X\) of this manifold the equality \(\text{ind }X = 0\) implies \(\text{Ind }X = 0\);
(b) for any closed subset \(X\) of this manifold the equality \(\text{ind }X = n\) implies \(\text{Ind }X = n\).
MSC:
54F65 Topological characterizations of particular spaces
54F45 Dimension theory in general topology
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