1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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 & Completeness

  1. Nov 15, 2011 #1
    1. The problem statement, all variables and given/known data

    I haven't been able to find any theorems stating the relationship between a totally bounded space and a complete metric space, i.e., whether totally boundedness implies completeness. (I know that completeness implies totally boundedness though). Is it true that totally boundedness implies completeness?

    Any help is much appreciated.

    2. Relevant equations

    A metric space is totally bounded if give any ε>0, there exist finitely many points [itex] x_1, ... ,x_n[/itex] [itex]\in[/itex] M s.t. A [itex]\subset[/itex] [itex]\bigcup_{i=1}^{n}[/itex] [itex]B_{\epsilon} (x_i) [/itex] where n is finite.

    A metric space M is said to be complete if every Cauchy sequence in M converges to a point in M.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Totally Bounded & Completeness
  1. Bounded functions (Replies: 0)

  2. Total Variation (Replies: 0)

  3. Totally bounded sets (Replies: 0)

Loading...