Geodesic
A differentiable manifold with non-coinciding dimensions under the continuum hypothesis
Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 151-162 Cet article a éte moissonné depuis la source Math-Net.Ru

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Under the assumption of the continuum hypothesis we construct a differentiable $n$-manifold $M^{n,m}$, $4\leqslant n, of dimension $$ m-1\leqslant\dim M^{n,m}\leqslant m<m+n-3\leqslant\operatorname{Ind}M^{n,m}\leqslant m+n-1. $$ The space $M^{n,m}$ is perfectly normal and hereditarily separable. 
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V. V. Fedorchuk. A differentiable manifold with non-coinciding dimensions under the continuum hypothesis. Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 151-162. http://geodesic.mathdoc.fr/item/SM_1995_186_1_a8/

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