1 1 1 1 Let A = + + + + 1+sin 1 2+ sin 2...

 

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1 1 1 1 Let A = + + + + 1+sin 1 2+ sin 2 3+ sin 3 n + sin n : ne N}. (a) Is A bounded? Is A closed? Is A compact? Justify your answers. < (b) Find an open cover of A with no finite subcover, if possible. (c) For any compact set BC R, show that AnB is compact. 1 1 1 1 Let A = + + + + 1+sin 1 2+ sin 2 3+ sin 3 n + sin n : ne N}. (a) Is A bounded? Is A closed? Is A compact? Justify your answers. < (b) Find an open cover of A with no finite subcover, if possible. (c) For any compact set BC R, show that AnB is compact.