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I am interested in finding some paper or book where i can find how to build an imbedding $e\colon M^n \hookrightarrow \mathbb{R}^q$ of an arbitrary Hausdorff topological $n$-dimensional manifold $M$ into some euclidean space $\mathbb{R}^q$, where the size of $q$ is of no importance. For general Hausdorff TOP $n$-manifolds, there are some results about imbedding in the book of Munkres of Topology, where it is shown how to imbbed a $n$-manifold into euclidean space of dimension $2n + 1$, however, these results are far stronger that only building an explicit imbedding and an explicit imbedding is never build, it is only shown that such an imbedding must exists.

In the case of compact TOP manifolds, a similar result to the one that i need can be found in the paper

D.B. Gauld. "Topological properties of manifolds". The American Mathematical Monthly, 81(6):pp. 633-636, 1974.

There, it is shown that a compact, Hausdorff TOP manifold can be imbedding in an euclidean space of sufficiently high dimension, the proof is simple and the imbedding is constructed.

Is there any paper or book where the construction of an explicit imbedding for Hausdorff TOP $n$-manifolds can be found ??

Thanks in advance !!!


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I know this isn't precisely what you want (it still seems to lack explicitness) but you might find this interesting:… Good luck! – Alex Youcis Sep 26 '13 at 6:58

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