Explore BrainMass
Share

Explore BrainMass

    continuous function

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

    Topology- Compactness
    Please do the problem #1. My textbook is Topology by James R. Munkres.
    The following are the contents covered in class so far. Do not use any knowledge exceeding them.
    (If you have more questions about my posting, communicate through the Message Center.)
    Sep-08-09 Session 1 Metric spaces and continuous maps.
    Sep-10-09 Session 2 Topological spaces and continuous maps.
    Sep-15-09 Session 3 Examples of topologies.
    Sep-17-09 Session 4 Closures, interiors, the Hausdorff axiom. Infinite products of spaces.
    Sep-22-09 Session 5 The quotient topology. Surfaces.
    Sep-24-09 Session 6 Connectedness and path connectedness.
    Sep-29-09 Session 7 Compactness.
    Oct-01-09 Session 8 Digression: knots, surfaces and all that

    © BrainMass Inc. brainmass.com October 9, 2019, 11:58 pm ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/topology-compactness-continuous-function-273970

    Attachments

    Solution Preview

    Proof:
    We consider any . Since is continuous, then for any , we can ...

    Solution Summary

    Assess as a continuous function. The expert examines compactness in topology.

    $2.19