engleski

Inverse limits of the Cantor-manifolds

We say that a compact space X is (n, k)-Cantor-manifold if dim X= n, and if for every closed subset F of X of the dimension dim F<=n—k the set X\F is connected. In the present paper we investigate the following question: Under what conditions the limit of the inverse system of the n-dimensional Cantor-manifolds is (n, k)-Cantor-manifold? The partial answers for the inverse systems with fully closed monotone bonding mappings and for inverse systems of metric Cantor-manifolds with open bonding mappings are given.

Inverse limit; Cantor manifold

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