Explore BrainMass

Explore BrainMass

    subset of S is compact

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

    Let S be the set [0,1] and define a subset F of S to be closed if either it is finite or is equal to S.
    Prove that this definition of closed set yields a topology for S.
    Show that S with this topology is compact, but S is not a Hausdorff space.
    Show that each subset of S is compact and that therefore there are compact subsets of S that are not closed.

    © BrainMass Inc. brainmass.com October 10, 2019, 2:00 am ad1c9bdddf

    Solution Summary

    This solution goes over mathematical concepts within the realm of geometry and topology, such as compact and closed topologies.