Geodesic
Minimal Subspaces with Maximal Dimensioanal Diameters
Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 219-222.

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Suppose that X is a compact metric space with dim X = n. Then for the n − 1 dimensional diameter dn−1(X) we have dn−1(X) > 0 and in the same time dn(X) = 0. It follows now that X contains a minimal by inclusion closed subset Y for which dn−1(Y ) = dn−1(X). Under these conditions Y is a Cantor manifold [7]. In this note we prove that every such subspace Y is even a continuum V^n. Various consequences are discussed. *2000 Mathematics Subject Classification: 54H20.
Keywords: Cantor Manifold, Dimensional Diameter 
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Todorov, Vladimir. Minimal Subspaces with Maximal Dimensioanal Diameters. Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 219-222. http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a21/