# Connected Annulus

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Prove the annulus A={z in (the set)R^2 : r <= |z| <= R} is connected.

Is it sufficient to show that the annulus is homomorphic to the circle, and then since circle is connected, so is the annulus ? If so, how do you show it, if not, can you shed light on another method?

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The annulus A is the image of the map defined as:

. Since f is ...

#### Solution Summary

A connected annulus is investigated.

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