MHB Is Limsup of Upper Semicontinuous Function True? Help Needed

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for any upper semicontinuous function limsup f(x)=lim f(x)...Is thıs true ? I don't know, please help me :)
 
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No,

Just think in $f(x)=sin(x)$, is continuous and its upper limit is 1 when $x\to +\infty$
 

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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