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 '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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