MHB Integral: Investigating Convergence II

maxkor
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Investigate the convergence of the integral
$\int_{0}^{\infty} \frac{x^{ \frac{2}{3}} + \frac{2}{3} \ln x }{1+x^2} \mbox{d}x$
 
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Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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