Explore BrainMass

Explore BrainMass

    Prove that union I: = Uα Iα is an open interval.

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

    Fix a point p in R. Let { Iα } be a ( possibly infinite ) collection of open intervals Iα = ( cα , dα )
    which is a subset of R, such that pЄ Iα for all α.

    Prove that the union I: = Uα Iα is also an open interval ( possibly infinite ).

    Hint: Consider c: = infα cα and d: = supα dα and show that I = ( c, d ).

    © BrainMass Inc. brainmass.com March 4, 2021, 6:12 pm ad1c9bdddf


    Solution Preview

    Please see the attached file.

    Since union of two open intervals which contain p is an open interval,

    where smaller of and
    and greater of and .

    Again ,

    Solution Summary

    This solution is comprised of a detailed explanation of the union of open intervals is also an open interval. It contains step-by-step explanation for the problem.