If a smooth manifold admits a finite atlas, then for many technical purposes it is as good as compact. I was surprised to learn that every connected smooth manifold actually has a finite atlas. This result can be found in

A. Solecki. "Finite atlases on manifolds", Annales Societatis Mathematicae Polonae. Series I: Commentationes Mathematicae XVII (1974)

A Google search reveals only a few references to this paper in the whole net.

**Question:** Why is this result/paper so unpopular? Are there alternative proofs that are more popular/cited?

Please note that this question is very different from the existence of a finite covering atlas for a topological manifold. The atlas here has to be in the given smooth structure.

Theorem: For every smooth connected manifold $M^m$ of dimension m>1 there exists a finite atlas consisting of at most $2\cdot 3^{2m}$ full charts. The number of charts can be restricted to $3^{2m}$ if $\partial M=\emptyset$, to $2\cdot 3^m$ if $M$ is compact, and to $3^m$ is $M$ is compact and unbounded.

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