Explore BrainMass

Explore BrainMass

    Connected Annulus

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?

    © BrainMass Inc. brainmass.com March 4, 2021, 8:11 pm ad1c9bdddf

    Solution Preview

    The annulus A is the image of the map defined as:
    . Since f is ...

    Solution Summary

    A connected annulus is investigated.