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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
##### Keywords:
nonmetrizable manifolds; inductive dimensions