Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Totally bounded but not bounded

  1. Mar 3, 2014 #1
    It seems strange, but would a metric space consisting of two points, X={a,∞} be totally bounded, but not bounded? because d(a,∞)=∞. But for all ε>0, X=B(ε,a)UB(ε,∞).

    It's been proven that totally bounded→bounded, so this is wrong. Why?
     
  2. jcsd
  3. Mar 3, 2014 #2
  4. Mar 3, 2014 #3

    jgens

    User Avatar
    Gold Member

    This "assumption" is incorporated into the definition of metrics.
     
  5. Mar 4, 2014 #4
    the axioms for a metric space state that for any two points in the metric space, their distance is a real (and finite) number.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Totally bounded but not bounded
  1. Compact -> bounded (Replies: 2)

Loading...