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## Main Question or Discussion Point

I am newbie to topology and trying to understand covering maps and quotient maps. At first sight it seems the two are closely related. For example SO(3) is double covered by SU(2) and is also the quotient SU(2)/ℤ

_{2}so the 2 maps appear to be equivalent. Likewise, for ℝ and S^{1}. However, I don't think this is true in the general case. Can somebody provide an**intuitive**understanding of the criteria for equivalence and how it applies to one of the above examples.