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If $M^n$ is a compact topological manifold (not necessarily with additional structure), is there an upper bound on the number of charts needed to cover $M$ ? Does this bound depend on the dimension of $M$ ?

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a related thread –  t.b. Dec 20 '11 at 6:42
    
I have seen a related thread about my question. But it seems the manifolds they talk about are triangulated manifolds and i would like to know an answer that does not depend on triangulability of manifolds. And i would like to have a good reference. Thanks in advance !! –  onebengaltiger Dec 20 '11 at 19:05
    
I have examined the related thread a bit more, and it seems i could find some answers by looking at Ostrand's theorem and Kirby-Siebenmann handle decompositions for TOP manifolds. Thanks for the tip about the related thread !!! –  onebengaltiger Dec 22 '11 at 5:11
    
If you still care about this old question: An upper bound can be taken to be $n+1$ (compactness is not relevant here). I do not know if this bound can be improved. –  studiosus Mar 15 at 3:28
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