Geodesic
A differentiable manifold with non-coinciding dimensions under the~continuum hypothesis
Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 151-162

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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 $$ m-1\leqslant\dim M^{n,m}\leqslant m+n-3\leqslant\operatorname{Ind}M^{n,m}\leqslant m+n-1. $$ The space $M^{n,m}$ is perfectly normal and hereditarily separable. 
@article{SM_1995_186_1_a8,
     author = {V. V. Fedorchuk},
     title = {A differentiable manifold with non-coinciding dimensions under the~continuum hypothesis},
     journal = {Sbornik. Mathematics},
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     volume = {186},
     number = {1},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_1_a8/}
}
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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/